I'm the Charles that Ferenc was referring to, and what happened to me is that I got a Stentor Graduate (their 3rd from the bottom model, a decent beginner's violin, by reputation) off Amazon for about $250, and was quite pleased with myself until I got it. It had a number of issues, and the worst one was the same one Ferenc had with his - if you depressed one of the strings (medium high up, on mine), you could only hit the strings on either side of it. The string you were trying to play wasn't reachable.

That was caused by the action being too high, and the fingerboard too heavily scooped. According to my luthier, that's dirt common, because the manufacturers are much more worried about getting returns for defects than making a really good violin at that price point. Getting the fingerboard flattened and the action lowered cost me about $250, plus another $100 of other work. So that really good deal I got ended up costing me $600 for the violin.  It's a fairly nice violin now, but I could have gotten a much better one spending my money another way.

So the advice I have for everyone getting a new violin is to make sure it is set up properly by someone who knows what they're doing.  If you get a straight-from-the-factory one, it's unlikely it will have had that done. (See the earlier comment about preventing returns.)

I've seen one online review on Youtube comparing the Bunnel and the Apprentice, and he rated the Apprentice better than the Brunnel in all categories. It wasn't by a large margin, but in all the ways he thought it was appropriate to compare the two, he preferred the Apprentice.

I've never played either the Bunnel or the Cecelio, so I have little hard data to go on (and I'd need to have played dozens of all three before I could begin to say anything with any certainty).

I've been very impressed by Cecelio's low end - the stuff around $100. Their stuff in that range is noticeably better than almost all of the competition.  As the price goes up, though, there's a lot more competition.

I would normally have argued for the Apprentice over the Cecelio except for that post Mark made about the used one.  I'd check with Fiddlershop and see if they've given that their standard setup. If so, compare what that one sounded like (not at all bad to my ear) with several of the Apprentices (you can find many examples by searching Youtube for "fiddlershop apprentice") and pick the one you like better.

The standard Cecelio's (even the 600) that Fiddlershop sells are NOT set up that way. They are drop shipped from Cecelio. (Meaning Fiddlershop takes the order, handles the money, etc, but the instrument is shipped directly from Cecelio to you - Fiddlershop never touches it.)  This one may be an exception. Even if all they've done is looked it over and said "It doesn't need any adjustment," you'll be better off than a straight shipment from Cecelio.

The tailpiece is a minor issue. The more it weighs, the more it leans the instrument towards the darker, richer part of the tone spectrum. (But that can also mean more muddy - your tastes will play a part in that.) The fine-tuners are a judgement call. The detachable ones mean you can take them off later, as you get better at tuning with the pegs (or get geared pegs). That's generally thought to improve the sound, a little.  The built-in ones are more likely to work without glitches, but you'll have to replace the entire tailpiece if you decide you don't want them anymore. A tailpiece is a $15 part. I wouldn't base my decision between violins on it.

The bows in question are another matter entirely. The Fiddlerman CF bow is a much better bow than its price suggests.  It could probably compete in the $150-$200 range.  The brazilwood bows that come with most beginner outfits is not nearly as good.

The wooden bow that I got with my Stentor is an exception - basically, I got lucky and it's a much better bow that you typically get with such violins. I'd even rank it as slightly better than my FM CF bow.  Nonetheless, I almost never use it, and I just bought my 3rd FM CF bow (because it was on sale).  The CF bows are near-indestructible and it doesn't matter that much if you forget and leave the bow tight.  The Stentor bow is nowhere near enough better than the Fiddlerman one to bother with the risk and hassle of using a wooden one.

I would contact Fiddlershop and discuss the Cecelio with them, vs the Apprentice. If the Cecelio has gotten the same setup that the Apprentice has, then especially because it comes with one of their CF bows, that might be a good deal. Even if it's just been inspected to make sure no setup like that is needed, I'd give it serious consideration.  If it hasn't been set up and could use it, discuss the cost of that with them, warranty, and similar such issues and make a choice.

Even if you don't buy anything from Fiddlershop, either buy from someone who WILL do the setup, or plan on around $100 worth of luthier work after you get it.