Amateur said
 
My question is, I'm quite a bit taller than average with a wide wingspan, would I be better off with a viola?

A viola will probably fit you better physically, but there are lots of people who are larger than the optimum size for a 4/4 violin and still manage to play one without too much trouble. Large hands (especially fingertips) will probably be more of a challenge than long arms.  (And people with small hands have their own set of challenges - violins are not ergonomic. )

Violas are (mostly) what I call oom-pah instruments. They play the background/harmonizing part, which sounds quite good in an orchestra, rather less so when you're playing by yourself.

There are several options:

• Go with a violin. This will give you the widest range of options for playing both by yourself and with others, and playing the parts of songs that are recognizable.
• Go with a straight viola, and play it as one. I, personally, don't care for oompah instruments (played one in band many, many years ago, and I've had my fill), but that doesn't in any way make them wrong.  The tonal register is more pleasant to some people (including me, actually), and there are a few pieces where the viola gets the lead.
• Get a viola and string it as a violin - I did this with a viola I got on an auction site. Once my teacher found out I had one, he suggested it, because I also am a little larger than average. I think the one I had (a 15.5") was a bit too large for me. The tone was also not the best, partly because it wasn't an especially good instrument to begin with, partly because I was asking it to play outside the range it was designed for.  This combo does give the sound of violin with the physical size of a viola, though.
• Get a viola, string it as a viola, but play it as if it were a violin. You won't be able to play with others much (you'll be a fifth low), but if you're only playing for your own pleasure, it will work fine.  This will also give you the physical size of the viola, while letting you play the melodic line. If you have no intention of every playing with anyone else, and trying a few violas makes them feel much more comfortable than a violin, this might be the way to go.
• Get a 5-string viola.  These aren't common, and the tone won't be as good as either a good viola or a good violin (the more strings you add in, the more compromises you have to make to the design), but it will probably sound better than a stock viola restrung as a violin. The other main disadvantage to a 5-string is that even though the neck is a little wider, the strings end up a little closer together. Especially if you have big fingertips, that can get tricky.

Amateur said
  This shop services violins for the local school programs and these are student level violins. Are these a good start for someone on a budget? I don't want to end up with a barely playable instrument again, I'll accept the compromise on tone and finish with cost but not playability.

If the shop has reworked them from how they came from the factory, then they may be decent starter instruments.  Unfortunately, an awful lot of places tend to consider student instruments to be things that deserve nothing good. The wood is cheap, the quality of the build is mediocre to poor, and how things are put together has a lot more to do with making sure it doesn't come back to the factory than it does the instrument being easy to play.

As an example, for my first instrument (bought before I found this site), I got a Stentor off of Amazon. I'd done a fair amount of research, and thought I was getting a fairly good instrument for the money.  Compared to most of the stuff out there, I probably was, but it had quite a few problems.  The instrument cost me $250. After $350 worth of luthier work, doing things like flattening out the fingerboard, lowering the action (drastically - I was building up calluses, which you shouldn't need to play violin), and a few other odds and ends, it was a much better instrument. It sounded better, and was massively more playable.

Many places will not do $350 worth of work to a student instrument, figuring it's not worth it.  Wherever you get one, make sure a good setup is included in the price. (A lot of what was done to mine goes beyond "setup", but a lot of places don't even do the $125-$150 worth of stuff to do a good setup.)

So wherever you get one, make sure a decent setup is included in the price. You're going to need it pretty soon if it comes without it, and it's generally cheaper if it's built into the price of the instrument.

Amateur said

Violin appears to have it's own obvious challenges but is it as frustrating as some make it out to be? As my name implies, music is my hobby, I don't intend to be a serious performer. I enjoy figuring out pieces and honing technique as much as I do playing a clean tune.  

There are very few techniques in violin that are hard to learn (vibrato is about the only one that comes to mind as a possibility, and that's more because you're making a motion that your muscles aren't used to, so you're clumsy at the start - the idea is straightforward enough).

There are two problems that make it challenging:

First, everything is approximate. You don't have frets with which to pick the note, and you don't have keys to sound the note. Both the left-hand fingering and the bowing (assuming you're using a right-handed instrument) are almost the same each time.  This extends the learning time dramatically, and can mean you don't get as good as you'd like to be for much longer that you thought it would take.

The answer to that is to do anything new (or anything you're having problems with) very slowly and carefully, working on getting it right, and letting things like speed come along as they will.  That takes a peculiar form of self-discipline that most people (me included) find very challenging.

Second, remember the old line about walking and chewing gum at the same time?  Playing a violin can seem like riding a unicyle across a tightrope, while watching an instructional video you'll be tested on later, while carrying on a moderately intense conversation.  In other words, you have to multitask a lot.

It is as common as dirt to learn a new technique, try to use it in a song, and have the last 3 or 4 techniques you've learned (and thought you'd mastered) completely come apart on you. I don't know how many thousands of times you have to practice various things before they become so ingrained that you do them right no matter what else you're doing. (I'm not sure I've practiced anything that many times yet.) But it's enough times that I can pretty much guarantee you'll run into this problem.

If you're expecting it to happen and don't get too fussed about it, it's not that bad. A few days practicing the new technique while trying to hold on to all the old ones, and things start integrating, and it starts sounding halfway decent again.  If you think that once you've learned something well enough to do it in isolation, while you're concentrating on it, then you've "learned" it and should perform it perfectly from then on... expect much emotional pain.

There's a good side to both of those. The violin (and the viola is capable of just as much, even if there's not much music like that written for it) can be one of the most expressive instruments there is.  The fact that you can hit the note a little bit sharp or flat is bad when you don't want to do that, but it's great when that's the effect you want.

As an example, I'm currently learning Schindler's List.  There's a middle section which is completely unlike the rest of it, and it sounded rather bad to me, in particular this one G#.  It just didn't fit with the rest of the piece at all.  My teacher told me that it was supposed to be played in something of a Gypsy style, and that G# was actually played more as a G## (not an A, about a quarter tone between the G# and the A).  It sounded immensely better.  You can't do that with most instruments. Even something like a guitar, where you could bend the note to get that effect, what if you needed to make it go a quarter tone flat?  Good luck bending a string THAT direction.

All of the forms of flexibility that make it as difficult as pushing cooked spaghetti when you're learning it gives you superb expressiveness when you've mastered it. I'm made the claim before, and I have seen nothing to convince me otherwise, that there has never been anyone who has completely mastered the violin - they know every technique possible, and can use any of them in conjunction with anything else and do so flawlessly.  It's a "deep" instrument. The basics aren't too hard to master (as you found when trying one in the store), but there will be new techniques to learn and new nuances to those techniques for a long, long, time.