Umgowa, I don't know a ton, but Sailor is right. Your cheese will fall thru. As long as you keep syphoning off the whey, it'll be fine. even queso fresco has a drying period, that is when the rind will form.
There may not be any need to sand off the burrs, there may not be any. I have had luck with using a utility knife and just knocking them off with that.
For your follower, you may have to go a tad smaller than 3 9/8...maybe 1/16 smaller? the wood will swell, and it may get tight. especially on long presses. I can't remember where I saw it, but someone said to use food grade mineral oil (pharmacy section, used for stool softener) and rubbing or even soaking your follower. I just put on 3 thick coats and a new thin coat if I have to wash anything (if whey comes in contact with it)
I think you are set! Good luck, and have fun playing with your new toy