Hi Ash,
There are many, many threads in this Forum which deal with the topic of mic choice. The answers are so varied, that they cannot be listed quickly and easily. Try a search and see what you can find.
But very briefly, you will find than many people use the ubiquitous Shure SM-57 for snare and toms. A good dynamic second choice for toms would be the Sennheiser 421. Many also like the AKG D-19. But others will use a condenser on toms.
For Bass Drum, many use the AKG D-112, while some prefer their older D-12. Others like the Electro Voice RE-20. Their are lots of other choices, of course.
For overheads/cymbals, many recordists like to move up to condenser mics, either large or small diaphragm. Many models abound here, and your budgetary situation would narrow your choice. You could spend anywhere from $500 to $10,000 on a pair of these.
Best of luck.
Lose the China.