As said above, the word "Benchrest" covers a lot of ground.
Go to different matches and see what you like. Different disciplines require different rifles to be competitive.
I'd suggest dipping your toes in the games with loaners or a factory class with your current rifle.
Once you get a good idea of what you want to shoot, though, I suggest buying a used rifle on top-notch custom components that is a known good shooter. At the same time, if you are shooting a discipline where they are used, I recommend getting and consistently using windflags.
A couple of the guys here got me started that way and it's been a gift that has kept on giving. Shifted disciplines but I'm still happily shooting that rifle (adapted from 10.5 to 13.5 lbs and from 6mm to 30 cal...for Varmint for Score (VFS)).
It's simple. A good rifle will teach you how to shoot buy removing the precision of the rifle from the equation. It's all you after that. Reading the wind, bench manners, load tuning, etc. A not so precise rifle will leave you wandering in the dark. It's like chasing a system with more variables than equations to nail it down.
I'll tell on myself by way of example...
I shot a local area club match this weekend. I had tuned my rifle to a gnat's hair the day before, so I knew it was shooting. My bench partner and I set my flags up super well, so I could read what little wind there was super well. The bench was set up well. But every two or three shots would flip a shot 1/4" to the left. Never the right. Zero vertical. I struggled with it for a while, but because I knew the rifle was a known quantity, the problem had to be me. Skipping a few steps, I figured out that I was sitting at a 45 deg angle to the rifle. The butt was hitting my shoulder at an angle rather than square. Now, if the butt is skidding to the right off my shoulder, where does that flip the shot? Yep, to the left. I squared up to the rifle, everything started going right and despite finishing in the middle of the pack, I left happy because I'd learned a lesson that I'll never forget.