As this one has been covered so many times in the past I was going to let Light field this one first this time, and then agree with him, but before we get to far into it here is my advice.
1. Do some searching here there is loads on the subject. You'll find that Light and myself STRONGLY advise against using nitro in a home setup unless you really know what you are doing. It can be very dangerous and for a small one off project there are much better options.
2. The Stew mac and LMI waterbased products can give excellent results if you use them correctly. They can be a bit more fiddly than nitro but they are worth the effort.
3 if you don't have spray facilities or are unsure about using rattle cans (they can be a bit unpredictable in the way they behave) then consider a brush or wipe on finish.
4. Tung oil is a good finish and natural. Even better is Tru oil. Despite the name it is not a true oil finish, it is closer to a violin type varnish and is entirely safe and very easy to get a good finish if you dedicate the time to it and are not after a mirror gloss. I offer it a finish option on many of my instruments I like it that much. It's a linceed oild based varnish with some modern polymers added.
5. I have never used oil based polyurethane on an instrument so I can't comment. I don't know what specific brush on finishes you guys in the States have available, but here Rustins Plastic Coating is very good. Many makers from small to medium have used it in the past as an alternative to hard polyesters. In theory just about any finish can be applied with a brush and then cut and buffed. Some are easier than others.
6. Before you even consider you finish you need to think about what sort of look you want. The timbers you have there provide some challenges if you want a flat clear finish. Ash is very open grain and will need some careful prep and filling if you want it flat and the grain filled. Purple heart can bleed colour into the finish and adjoining wood with some finishes. When you get to it pipe up and I'll give you some tips depending on what finish you opt for.
7. Whatever you do test on scrap first.
8. Whatever you do test on scrap first.
9. Whatever you do test on scrap first.
10. Go back and re-read points 7, 8, and 9, they are very important.
I'll step back and let Light steer you away from nitro as well now, but before I do, donkeystyle who told you this?
the theory behind nitro is not only does it yellow and age in an interesting way, but it's wood based, so it (in theory) doesn't get harder or stay softer than the wood which allows the wood to resonate to it's full potential.
It's rubbish. Not getting at you, it just it aint true.
As to the effect of a finish on an instrument. You are going to notice differences on acoustic instruments more than electrics and you can never really tell how much effect it has even then. As a rule you want as little as possible to give you a durable lasting protection to the wood. In the case of your first instrument go with whatever is easiest and keep it simple first time.
Having said that if any finish does kill the tone of your wood it would be polyester. I'm not to keen on the Urethane finishes I've seen either but on a first instrument thats not your biggest concern IMHO.