I'm pretty new to photography so sorry if some of these questions seem silly.
I have a Canon Powershot SX530 HS and I'm trying to get more into portraits and landscape shots, what are some good lenses for these purposes that would work with my camera?
"...what are some good lenses for these purposes that would work with my camera?"
I have not personally used a Powershot SX530 HS. But I think the lens you have is fixed and can not be changed.
For landscapes stay on the lower FL numbers and for portraits somewhat higher FL numbers perhaps 35mm. The big problem with these very small sensor cameras is getting a true WA view.
Using these cheap adapters on fixed lens Powershots can be damaging. If you choose to use them do so with great care.
The fact you have a fixed lens camera is indicates a good reason to leave it as is. Just learn how to use what you have. Get a good post editor which will do much to all the filter work you may want.
Now although the camera lens on the canon sx530 is fixed, you can buy adapters that allow you to put on filters. This link will give you an adapter for the canon sx530. i do not have it personaly but i have seen people who love them.
It has a 67mm thread size so you can buy filters, hoods and other things that can go on it.
Those adapter rings work very nicely with the lightweight filters, but be cautious about using teleconverters or wide angle/macro lenses on it. I ruined a camera with a teleconverter because it was too heavy for the focus motor to deal with, and also knocked the lens alignment out. Kept getting lens error message after that. Filters don't seem to be an issue.