I am looking for an engine that is powerful + cheap engine that will work in an ultralight aircraft and fly 1 person as well as the plane. yeah, this is kinda specific, but I have a tight budget and want it to be safe. 😬 thanks a lot if you can solve this for me!
Your best bet is to go with a motor developed for paramotors with all the grief of development already accounted for. They are big on static thrust and use small engines with simple and reliable reduction drives running fairly large propellers, mostly 2 stroke although there are some 4 strokes available now, like the EOS (if you want really decent reliability, you really need to go with 4 stroke). Root around in the paramotor world on the intertubes and educate yourself.
For an ultralight, you would just need to use a propeller with more pitch than used in paramotors due to the higher speed range, but otherwise these motor packages are ideal. You could purchase a used paramotor cage unit just for the motor/reduction drive for probably a lot less cost, for decent reliability, than the alternatives.
This is a homemade UltraLight airplane being tested with two pilot with different weight: 70kgs and 120kgs. It is using Simonini Mini Evo 2 (just use Google translate to translate the discription there).
Simonini Mini 2 EVO: a 2-strokes single cylinder engine, 33HP (or 25kW) at 8000rpm. Dry weight: 19.3kgs. Made in Italy. This engine is quite cheap, most used for paramotor as John K explained in his comment.
An equivalent engine is Rotax 377. It is 35HP engines @6500RPM. Weight: 34kgs. This is seems stronger than the Simonini as lower RPM, but heavier. Made in Austria. Unfortunately, it is no more in production.