The engine you're going to use isn't going to work under any circumstances.

Scratch building an airplane to try and save money will also not work under any circumstances. Even if you could build cheaper than you can buy (which you can't), you'll likely wind up with an unflyable airframe due to beginner errors.

Every beginner who wants to fly a fuel powered airplane needs to start at the same place: An ARF or RTF trainer with a .40 sized glow engine. The plane and radio and all the gear will set you back around $600 in the US once you allow for incidentals and memberships. There's no way to do it cheaper than that unless somebody gives you stuff.