I'll bet you Google these and find lots of info. Some possibilities are:
1000 yd Benchrest
(1000 yds. Requries advanced handloading skills and very spendy equipment to be competitive. I did this for a while)
(200-600 yds. Not as spendy a 1K BR and no need to handload for a while. I did this for a couple of matches)
M-1 Garand Matches
(200 yds. Cost can be reasonable. Not sure if you can handload for these matches or not.)
(I think it is shot at 600 yds. Equipment cost could be more than with Highpower. Handloading almost a must)
(100-200 yds. Requries advanced handloading skills and spendy equipment)
(Not to bad on equipment costs, handloading usually required, requires an incredible amount of skill)
(50 yds. No handloading required but lots of ammo sorting. Equipment can be spendy. Guys who shoot this class seem to be angst junkies.)
(Not sure of range 100 yds maybe? Cost not to bad.)
I recommend you find some local competitions that are appealing, then go watch some matches and ask the participants question (of course, not while they are shooting.
I wanted to shoot Centerfire Silhouette in 2005, but 1000 yd BR fit my schedule better. So I showed up with my sub 1/2 moa varmint varmint rifle in 6mm Rem and finished last. I think I managed to shoot a 10" group that day. I also ruined the 6mm barrel. I then built a 6.5x284 on the same Rem 700 long action I had for the 6mm, got a proper barrel, got a proper scope (Nightforce 8-32x56 BR model), found an okay stock, bought a proper front rest, and for the next year I usually finished in the middle of the pack.
The fall of 2005 I had to deploy for four months to the Middle East and during that time I had a rifle built. I used a proper action, proper barrel, and proper stock. I also bought a high end chronograph. The rifle cost about $2800 to build, which is on the low side for a competitive rifle. It took a couple months after I got back Jan of 2006 but I finally found a good load and then did very well in competition.
While I was shooting 1K BR I scrounged together the stuff and shot a couple of Highpower matches. Because I had friends helping me out I got into this sport way cheaper than I should have. I only had around $600 into the rifle (1x8 twist AR-15 with 3000 rounds though the barrel) and it would shoot 1.75" groups at 200 yds. I was given a shooting mat, a shooting glove, a shooting jacket, and a spotting scope stand. I already had the spotting scope. I moved away from the area before I had a chance to develop any real skill in Highpower.
I posted all that so you could see how one guy stumbled into competition shooting and progressed. I haven't competed since I moved in 2007 but I sure learned a lot about shooting and handloading those couple of years.