Will your budget stretch to a bottle of argon and a TIG torch? You can convert a stick welder to do scratch-start TIG. If you had that you would be off to the races. You don't really need any other tools. I basically use an angle grinder with cutoff wheels and flap disks (OK I'm a pleb but it works) plus the TIG and that's it. You can make a few simple jigs and fixtures with what you have.

If you can weld round mild steel tubing (presumably about 1.6mm thick) with your stick welder (probably want 6013 rods) and do a decent job then you can indeed build a basic frame that way. Scavenge the head-tube and BB shell from a scrap frame. They are quite thick metal so this is reasonable to do. Start by making some test joints and test them to destruction (won't tell you anything about fatigue but is a start).

Quality bicycle tubing is about half that thickness and not feasible to weld except with TIG.

Another type of fun project that people often do with stick or MIG is making things like cargo bikes, which are based on modifying an existing frame. Maybe a good place to start. I highly recommend this YouTuber below called Albert Nario. I think he's in the Philippines. He has awesome skills with very basic tools and stick welds everything.

https://www.youtube.com/channel/UChv...QaWdHJKtVet-9Q