I certainly don't want to put a damper on your dreams of designing your own plane (I have that dream myself) but you should certainly consider whether or not there are some existing designs that meet your needs, at least as a first project. With your A&P training, especially if you are in a program that teaches welding and woodwork as well as sheet metal, you have the skills to tackle many tried and true steel-tube fuselage, wood wing designs. I wouldn't get too caught up on range or speed, especially if you go with an open cockpit, as I think you'll find your bladder or comfort level in general will give out before the fuel supply. Cost may be an issue, however, as $20,000 doesn't go as far as it used too, but again your A&P training should let you tap into skills and opportunities for inexpensive engine rebuilding, for example, that the rest of us don't always have.
Off the top of my head, here are a few ideas for two-seat biplanes that might fit the bill in no particular order:
- Hatz CB-1 (including the newer Bantam model for the Jabiru 6-cylinder engine)
- Steen Skybolt
- EAA Acrosport II
- Stolp Starduster Too
- Fisher DH Tiger Moth replica
- Ragwing DH Tiger Moth replica
Any would provide a fun aircraft, and all have a successful track record, but it will depend on your likes, budget and especially engine options.