Unity has a free version with restricted features, your allowed to earn upto $100000 with it before they insist on you using the full version (by which point 1500 per year is nothing). For such a good engine aswell $1500 is nothing.
UDK non-commercial is free, $99 + a percentage of sales allows you to sell commercial games with it, a certain amount of revenue you have to pay the full license which makes $1500 look like pocket change.
Either way, if your just getting started in game dev then this might be a too big project. And the graphics quality of a game will very rarely depends on the engine, its more to do with the quality of the models and textures you put into it, although unity aswell as offering an engine have a web store where you can buy licenses to use various assets in your own projects. Just downloading a model from somewhere and using it is usually against copyright law, unitys webstore you can buy them legally to use in any engine, not just unity, but they might not be cheap.
Do you have any programming experience at all?
I currently know C++ some Java and a bit of Python (Still playing around with the language a bit). As for the textures and models, I use Blender (I have been using it for around 3 years now) So the models won't be a problem, textures are all created in gimp or paint.net! (I am all about free stuff!) I have just been having a war in my head about what engine to use, and I didn't know that I could use Unity for free up until 100,000$, I looked all over the net trying to find the most cost effective way to do this project. It is a bit daunting but I think the hardest part of this project won't be the models or story but the game-play itself, I want it to be fun not tedious or boring. Thanks for the quick input though!