As an 18 year old student you are not going to be wanting to live by yourself in a Melbourne apartment.
If you are studying then most likely you will have an income of about six hundred dollars a fortnight (youth allowance plus six or eight hours of work per week). If you want a one bedroom apartment in a suburb worth living in, you will be looking at paying two hundred dollars a week minimum. So that's most of your money gone right there. I live in a tiny, one bedroom apartment in the worst part of Richmond (which is otherwise a pretty cool suburb to live in) and I pay $240 a week.
Also, you will not get an apartment on your own. The rental market here is tight as, and there will be people competing for one bedroom apartments that have full time jobs and don't come from the riskiest demographic to rent to (ie, you.) Much better to find a sharehouse, pay half the rent and meet some people while you're at it.
St Kilda is mostly pretty expensive and pretentious. Carlton is cool but very close to the city meaning it's very popular and hence can be expensive, but if you can find a sharehouse there it would be good. Generally the best places to look are around the inner north. Places around the Northcote or Brunswick area are pretty cool, close enough to the city, and relatively cheap (especially in comparison to St Kilda). If you want to go way out you could find something quite cheap but it would be in a boring shitty suburb ages away from anything.
Weed here is exactly the same price and quality as anywhere else I've lived (although I've never lived in Perth).