Hello and welcome,
As noted above you're not the first young person to join here and ask a similar question. Back in the old days we had shop class where you could learn metalworking skills, not sure if your school district offers anything but if they don't you could look into what it would take to get into a program at community college.
www.dallascollege.edu
That may be a way for your folks to see how serious you are and maybe give a litte space in the garage for your use.
As for benchtop machines, I wouldn't rule them out. There are many folks who do great work with the RF30 mills like I have. They are plentiful and can be had for short money if you are willing to wait for the right deal. But, you can also do a lot of good work with just a lathe, or even a bench grinder and file. If you want to make things really the only limitation is your imagination.
Post a few pictures of the machine you're working on if you can.
John