Do not expect to try out for sniper school until after you have at least one deployment in most cases. There are plenty of Marines in line ahead of you, so learn to wait your turn.
Why would you think that you are just gonna enlist and all of a sudden become a sniper? Who the hell are you kidding? Just because you are a hunter, love to shoot, or have fired weapons since you were very young, this does not mean shit to the Marine Corps. Being the air-soft champion for your state or being the best paint-baller in your weekend club also does not mean you will amount to anything when it comes to Marine Corps marksmanship.
Some people who know how to shoot before enlisting can pick up bad habits and this messes them up while for others it doesn't effect them. In the USMC you are shown how to fire your weapon step by step and those who have a blank slate usually do better. Being a sniper is a lot more then sniping. You can be used in various manners, so please do not think that being a sniper is anything like any movie or video game you may of seen or played. There is a lot more to being a sniper then what you think, this I guarantee you.
Don't forget that potential snipers are screened to ensure that they have a higher level of maturity then their peers and they must be above average in their physical abilities (PT, CFT). Snipers are also rational and good thinkers and they must be able to communicate without sounding like a jack ass. It's not just about being a good shot. You must be the complete package which is why very few of you will ever meet the many qualification.
Enlist into the 03xx/infantry MOS field and just do your best. Once in your permanent unit you will see how the process works and you'll have a much better understanding of what is possible and what is not.
The Marine Corps isn't going to let you go to sniper school just for shits and giggles. Sniper slots are reserved for those who need it and not those who want it just to be cool.
Yes, reservists can also try to become snipers. Once in your reserve unit, you'll be able to ask your senior Marines how this process works.