First, there are 3 different classes in CMP RFS competition ("T" class, "O" class and "tactical" class) so you will 1st need to choose which classes you wish to compete in and that will effect which rifles to choose from. Then you need to decide as to which type of rifle you feel most comfortable with - bolt action or semi auto.
Most of the rifles that you will see at local matches and even at the national level will either be the bolt action CZ rifles (452 and 455 models) or the Ruger 10/22 platforms.
For "O" class a very popular bolt action rifle is the CZ 452 "UltraLux" which has a longer barrel and therefor a longer sight radius. They don't make the 452 "Ultralux" anymore so you would have to find one on the used market. They will usually run between $ 350 -$550 these days. You will need to put about $ 20 into the trigger but you will end up with a gun that can easily compete at the national level. If you go with a Ruger 10/22 platform in this class you will probably want to go with high comb wood stock, a longer barrel, a different trigger and probably a different bolt as well as a decent sight to be really competitive. Besides the cost of the gun a barrel will run you about $ 200-$300, a good top end trigger (Kidd 2 stage) will be $ 300 and a bolt will run you another $ 100 so that should give you an idea of what you are looking at.
For "T" class the same is true as above except that the chosen bolt gun has been a CZ 452 "American" model which are also not made anymore. CZ does make a 455 model American but unfortunately they now make it with a synthetic stock which will probably be too flexible so again the used market would be your best bet. 452 Americans usually run around 400-600 these days. Here is an ad to take a look at.
http://www.gunbroker.com/Auction/Vie...Item=332367678
You will only need to put on a scope and rings and $ 20 into the trigger to be competitive at the national level with this gun.
The Ruger 10/22 platform is also super popular in this class. As above - you will need to put some money into it for it to be truly competitive. Usually a barrel ($ 200-300) , trigger ($ 50- $ 300) and bolt ($ 60 - $ 100) are the usual modifications. I would also go with a high comb stock like the Boyd's "Tacticool" stock (which is what I will use this year) which can be picked up for $ 90.
Now the "Tactical" class. You will want to use a Ruger 10/22 platform in an aftermarket AR looking stock. Last years National champion (Our very own Ron V.) uses a Ruger 10/22 in a Nordic chassis which is also what I use in the form of a Ruger SR-22. As above - you will have to put some money into it for it to be competitive but you will end up with an absolute laser that is extremely competitive at the national level. The nice thing about using the Ruger platform is that you can go at your own pace and add one piece at a time.
Here are the modifications that I did to my Ruger "Tactical" gun which is also applicable to the other classes as well as the prices to just give you an idea.
Ruger SR-22 rifle - $ 420
Kidd 16.5 inch "lightweight" barrel in black - $ 200
Kidd scalloped bolt - $ 100
Kidd 2 stage trigger - $ 300
Kidd bolt buffer - $ 5.95
Kidd reciever pin kit - $ 30
Kidd cocking assembly - $ 36
Dave Tubb custom grip - $ 45
Leupold 3 X 9 X 33 Rimfire AO EFR scope - $ 350
Leupold 1/4 MOA target retical and M1 turrets added to scope - $ 200
DNZ forward mount scope base - $ 85
Modified hand guard and scope mount to lighten - $ 50 of machine work
For my "T" class rifle I just pull the barreled action out of my above "Tactical" gun and swap it into a Boyd's "Tacticool" stock and change the scope base and I am off and running without having to buy 2 guns. Only takes a few minutes to make the switch.
If you decide to go the Ruger 10/22 semi auto route you will want to spend a lot of time in this web site. A real candy store and the best in the business IMHO.
http://www.coolguyguns.com/
One last thought for you - Whatever you do - don't scrimp on the optics. Ron V. recommended that I get the Leupold VX II 3 X 9 X 33 Rimfire AO EFR and he was right on the money. The scope is perfect for this sport. I do however like the 1/4 or 1/8 MOA target dot as well as the M1 turrets. With modifications this brings the scope to about $ 550 which aint cheap. Leupold has now come out with their newer model now which is the VX2 instead of the VX II. Another good option is the Nikon 3 X 9 X 33 AO rimfire which is much cheaper at around $ 189.
Also - don't forget to save some out for the extras that you will need.
Things like
1. Shooting mat -
http://www.creedmoorsports.com/shop/...oting_Mat.html
2. Spotting scope -
http://www.creedmoorsports.com/shop/...ING_SCOPE.html
3. Spotting scope stand -
http://www.creedmoorsports.com/shop/...gal_Bipod.html
4. Sling -
http://www.mcssl.com/store/turnersad...8f73595b8db0b0
5. Sling swivel -
http://www.midwayusa.com/product/139...ing-swivel-set
6. Shooting glove -
http://www.workwear1.com/browse.cfm/4,1514.html
7. Extra ammo magazines
Anyway - hope this helps a little and if you have any questions let me know. I'm sure others will chime in shortly also.