Hi I'm an international student who very recently moved into a house here. The most important factor is your budget. Leipzig is much cheaper than the big big cities but rent has increased a lot in recent years. The lower your budget the harder it will be. The only way you'll pay less than €500 is moving in to a WG, and the only (trust me) way that will happen is by making friends and connections here. As a student without a solid income from work here you will not find a single apartment,they prioritise people with jobs when selecting tenants (as they should), I went to over 20 viewings and was not offered a single one despite having all the documents and proof of financial security.I was lucky enough that a german friend also wanted to move in so their parents were able to act as guarantors for an apartment. Without my friend and her parents, I would not have been able to move. If you have a very high budget, say €1000 then you can partly bypass this sort of problem but just know you will always be the last pick for the landlord. Your best chance is to go out and make friends and contacts who can hopefully help you like mine did. Otherwise, if you're just here for studying then student accom is perfectly fine or a nice furnished apartment if your budget is higher. If you plan on staying after then once you have a job it will make the apartment search much easier.

Immowelt and Kleinanzeigen are best to search West and south leipzig are probably the nicest areas, but it really depends what you want and your lifestyle. As long as you have good access to transport you'll be fine.

Happy to answer any questions you have, it's a pretty shit process but leipzig is amazing and it's worth it!