You said your violin is a neutral. I would try brightening it first. Not because I don’t like warm sounding violins. That is actually my preference. I tried a Scott Cao violin, not sure which model, when I went violin tasting. That is when I bought my lovely warm Rudolf Doetsch lovely violin.

The reason I say try brightening first is because that is easier to hear. I have my Rudolf, a Mendini 300 and a Windsor (similar quality as the Mendini). The Mendini and Windsor are low cost students with very very nice sound, although not bright or warm. I think it is the projection that makes them sound great with factory strings, but the sound itself is neutral.  Rudolf, being a higher end violin (considered intermediate if that means anything to you) has a nice projection of a lovely warm tone.

I put Pirastro Tonicas on the Mendini after I bought it. Wow, what a difference. Lovely sound. I tried a warmer string, Violino I think, but could be wrong. Did not work so well on either of those. The projection and clarity diminished greatly for some reason. They need that bright sounding string. Not sure where Tonicas fall on the charts, they differ on different violins anyway. The Mendini and Windsor each have their projection of bright sound characteristics, which I was not clear on when I received them because I could not tell. The Tonica strings found their “character”. I am quite happy with them for fiddle or upbeat songs.

That said, I had Obligatos on my Rudolf Doetsch for a little while. I liked the sound but found them hard to play on and sounded muddy to me. Muddy meaning, I needed to hear more of the individual notes for learning intonation. The sound itself was very pleasant. I now know why some strings are considered good for students or intermediate students or professionals (even though it is not set in stone). I think the Obligatos response was not as fast as I needed it to be. Maybe because of the way they are made to produce a warm tone? I never had that experience with brighter strings.

I put the original Dominant Strings back on my Rudolf, but am using a Kaplan Non-Whistling E. I tried and liked Fiddlerman. Nice warm sound. I will put my  Fiddlerman ones on again after I wear out the Dominants. I liked the Fiddlerman strings when they were on. They highlighted my warm violin’s warm sound, but I decided it was time to use up my strings before purchasing or using new ones and put the original Dominants back on. I think I will put my Passione E back on though. Love that E violin string. The Fiddlerman strings were on sale, so tried them. Like them a lot. I have set the Obligatos aside until I get better. My little reward. 😁

So, I would try the bright end first. Get the character of the tone of the violin out. Make it sing. You will hear it better, in my opinion. Then, try warmer.

You don’t have to go the expensive Obligato route. Fiddlerman strings are on the warm side, Violino (pretty sure that is the name. Made by Pirastro) are on the warm side, warmer than Fiddlerman. Neither is as expensive as Obligato. And maybe you want to work up to the extreme warmer sound. There are others that are warm and not the cost of Obligato. If you decide you like the warm, you can always step up to Obligato, but they are harder for students to play on.

For bright, try Tonicas first. If you like the bright, you can always step up.

As you can see, everyone has their opinion,  and violins have their own reactions to strings. What works for one, might not work for you. It seems to me that since you are going to do both and don’t have a preference as to which to do first, and you have already decided on Obligato and Evahs, just roll the dice and take whichever wins. Write both on separate scraps of paper and draw one out of the hat.