What is the cost range for converting to tubeless tires on a mountain bike?
If you have older rims that you can't set up tubeless for some reason. ( i.e. pinned not welded joints), there is the rather unfortunately named "ghetto tubeless" setup option. There are two main methods for this:
use an inner tube from the next smaller tire size (i.e. 24 in for 26 in), inflate, mount on rim and then cut along outside diameter so the tube folds over the rim. Trim and then mount tire so that it overlaps.
Use layers of gorilla or similar packing tape to completely seal the rim up to the side walls.
Neither of these is a complete description, I suggest you google for more detailed methods. I wouldn't use either of these methods for tire pressures over 40 PSI.
For any MTB rim/tire that has been made in the last 5 years or so that I have tried, I've had good luck setting them up tubeless for low PSI just using sealant and a standard rim tape/valve kit. The sealant does a reasonable job of sealing the sidewalls on even non tubeless ready tires.
There are a bunch of tricks to getting "standard" tires to setup and seal enough for the sealant to do its magic. If you want things to just work, tubeless ready tires and rims make the whole thing much simpler.
Technically you would need tubeless ready rims, tubeless ready tyres, sealant, rim tape and a valve.
If you were in a position to rebuild your current hub, you'd save money just by purchasing a rim.
Stans for instance, provide rim, tape, valve and sealant, and depending on the spec, all that, including Tubeless ready tyres could be had for GBP250 (both rims, tape, sealant, valves and tyres).
Arguably, you could call it a day there, as long as you are competent to swap a rim to an existing hub and spokes. When out riding, all but the extreme fearless will still carry a tube and canister in case of a puncture that cannot be solves by sealant alone.
However, in 6+ years of both MTB and Road tubeless tyres, I've never had a puncture in either that hasn't been solved by sealant. In fact, tubeless allows you to run lower pressures too so the likelihood of a puncture occurring is less.