Shellac is a slightly more natural product, being derived from fossilized bug poop. It starts out as some sort of waxy flake and is mixed with stuff like mineral spirits to apply as a finish. You can buy it as the flakes and mix it yourself, or a can ready to go or a spray can. Different woodworkers have different recipes for shellac based finishes and how to apply them, for what I do a spray can is fine. One of the neat features of shellac is that each layer melts into the layer before it, you don't have to sand as much between coats and will get a more even finish if you have to do repairs in the future.
Poly is a totally man made product. The difference between a brush on and a wipe on is the thickness. Poly is deluted with mineral spirits or the like and made thinner to brush on, make it thinner yet to spray on.
When I use poly, I typically use Minwax. It is pretty easy to find everywhere and is usually the cheapest.
When finishing most projects my two biggest concerns are easy and cheap, hence my recommendations.
I tried oil but finding places to put the pieces until they were dry was a pain, plus the timing thing. If I oiled something I had to wait a day or more to have it done. I like to start a project Saturday morning, spray it in the afternoon, put the finishing touches in the evening and give it away on Sunday.