Yes, Savage MKII FVT is a good rifle, but I'm not sure its going to be competitive for smallbore competition.Its a good training rifle at the very least.
For $600, you can get a Kimber 82 from CMPwhich is a full blown smallbore competition rifle- it will be competitive with the Anchutzes and Winchester 52s and only costs about 1/2 to 1/3 as much. http://www.odcmp.com/Services/Rifles/caliber22.htm

Winchester 52s, if you can find one, are well out of that price range.

Mossberg 144s aren't easy to find either, but are usually under $300. They are not a very well known rifle, but were made to compete neck and neck with the Winchester 52 target rifles. I use a Mossberg 144 LSB for practicing positions for highpower rifleon the cheap. Using midgrade mach ammo (Wolf)Ican put 5 shots into a hole the size of a pencil eraser at 25 yards (using iron sights).

If there are smalbore matches held near you, go to one and see what people are using, a lot of guys will let you try their equipment out.

If you are serious about competition (I'm not about smallbore- I use my rifle for training like I said earlier) the cost of a rifle is big, but you won't get anywhere if you handicap yourself with a rifle that doesn't fit your right, or isn't up to snuff.