What you want in a welder, of any price, is a wire feed or mig. Brazing good too of course, but a cheap ass hundred buck wire feed welder can still build a strong bike. the thin wire and using the lower power setting makes welding very thin tube easier by far than a stick welder.
Some tube still a bitch to weld, like very thin cromoly bike frames. Cheaper bikes with thicker mild steel tube are easy as pie to weld on.
Just practice on some junk bikes, or other very thin tube steel to begin with. Projects like a sturdy rack a good starting point.
I weld about as good as a monkey on LSD,, but I can still build a sturdy bike with a $100 wire feed welder that plugs into 110 volt plug. Harbor freight cheapo welder, but it's now built /modified 4 bikes. Using the 220 powered harbor freight welder was easier,, the welder just works smoother, but if you only have 110, the cheapo welder will do.
You may have a bigger budget, and if so,, then buy a more expensive, higher quality wire feed or mig welder. I'm sure the rule of thumb with tools applies, better quality tools make the work easier. But if you don't, the low ball welder can build a bike, easy enough for a total novice with welding like me to do it.