As a single PR, what property can I purchase to stay in?

There's a pretty comprehensive guide on the kinds of property you can buy here (under "If you're a Singapore PR"), but in short:

• As a single PR, you can't buy an HDB flat on your own. You can only do so with another family member who's also a PR (but you must both have been a PR for at least 3 years)
• Your best bet is private property (condos and such).
• You should have at least 25% of the condo's purchase price in cash savings/CPF OA. You'll need this for the downpayment since the bank will only loan you a max of 75% of the purchase price. But aim for more than this, since you'll also need to pay for renovations, furniture, lawyer fees, bank mortgage legal fees, buyer stamp duty, and so on.
• How much you should be earning depends on the cost of the property + how long a loan tenure you want. To be on the safe side, the general rule of thumb is that the mortgage payments should only take up 25% of your salary. (Most banks have home loan calculators so you can check what the monthly payments are in just a few minutes.)

I assume you are referring to Singapore PRs.

There isn't a restriction for purchasing private properties.
However, if you are referring to HDB, then is either you are 35 years old or above, else must be a couple with another PR or Local.