Normal hammer drill is not that expensive. Nowadays most have speed control and advertised as it can be used as driver as well, but I think you are better off with separate driver. More flexible with torque adjustment and more precise speed control.
These is what I just Googled. Even if you buy both, it is still way below your budget. If you buy no known brand, even cheaper
Instead of hammer, this is rotary hammer which is more recommended by many here. It has 3 functions; normal drill, hammer drill and chisel
https://shopee.com.my/STANLEY-SHR263KA-26MM...56835.295024301For driver, I'd recommend cordless one and this is not bad price for brushless motor which is popular now because can last longer and no need to replace carbon bursh (wear and tear part)
https://shopee.com.my/-ORIGINAL-STANLEY-18V...0120.5712010061I'm not a Stanley promoter

, but the good thing about them is Stanley has 2 years warranty. His bother, under Black and Decker, which is more for occasional DIY like you has 1 year warranty usually.
You can search around. There will be other shops that sell cheaper, but probably some come with no casing and something like that. Just double confirm. You can also search for other brand if you like Bosch, Hitachi but they are more expensive but shorter warranty

Oo that's cheap. I thought they are expensive. I looked at Makita before this walao so expensive