The best surfspots to surf as a beginner are Kabalana beach (Ahangama), Weligama beach (Weligama) and Detawa beach (Galle). Along the beach are many local surfschools with equipment that will get you started with the basics for your first surf lessons.
The best surfspots for intermediate surfers are Marshmellow (Ahangama), Lazy Right (Midigama), Fishermans (Weligama). All of them are reef breaks breaking off the coast, offering clean and mellow waves. Before going to these spots on your own, hire a local surf teacher to help you navigate the crowds and learn how to surf them safely.
The best surfspot for advanced surfers is The Rock (Ahangama), The rock gets the most amount of swell of any surfspot in south, therefore it is more exciting for the typical advanced surfer which doesn't enjoy the regular shoulder high waves in other spots. Be aware of the crowds, always very busy.
If you like critical waves and chasing barrels is your thing, then Rams (Midigama), Madiha left (Madiha), Mainpoint (Hikaduwa) are your best bet. These spots are breaking on dry reef and have often barrel potencial with a bit of off-shore wind.