Learning to weld is a skill thats worthwhile in itself. The thing about welding up a steel frame is that unless you are careful it will distort with the heat. The mistake that most beginners make (and I include myself in that as I'm not an expert welder, I just get by) is to try and weld too much in one go. The trick is to tack things in place then go back and fill the gaps so to speak. You dont need to seam weld everything. Personally I'd go with a MIG welder rather than an arc/stick welder. Its easier to strike the arc and get a good finish. While a steel box won't necessarily improve accuracy it will improve rigidity and you can still use wood with steel; a basic 4-sided bed with 4 legs of steel and a carcass of mdf bolted over will give it rigidity (and turn the base into a useful cabinet)