I was Pretty uncomfortable learning on someone else's plane too but it did help me kinda pay more attention to what I was doing when flying it. If you think you would be more comfortable flying your own --Go for it but I will tell you that a smaller plane won't equal less expense i mean relatively bigger does cost slightly more at times but they all cost you in a crash. Small or big they all hit the ground in the same way, also keep in mind that bigger does fly better( at least I think so) and is easier to see for most
I recently started back up in this hobby after about 20 years and I started out with an electric E flight apprentice good plane to relearn too fly with but I want a little more noise with my flying lol, then I started flying my instructors pieced together telemaster ( what a great plane that thing is ) back in the day I built all my planes so I Purchased a Balsa usa Student Trainer Its more of a building trainer but the plane is a perfect first nitro and I have been more than pleased with the build, haven't covered her yet but im sure it will be a great flyer
Sounds like your learning the hobby the best way possible you will get much farther with lessons such as you are doing. Welcome to the fun and keep us posted of your progress