Hi there,
Studios can be really expensive depending on where you are at uni, so I would first look and see if private studio's are in budget or not as they would be the best option. If that's totally out the question, then I'd look at post-graduate only flats in the area.
Most uni halls offer PG flats, as they tend to have longer tenancies due to having to be in uni over the summer. I know you said you can't go to uni halls because you need parking - I'm not sure where you're at uni but most places will have a dedicated few halls with parking availability at an extra cost, so I'd check if that is also an option.
For private accommodation, I believe you can still request to be put with postgraduate students, as they also tend to have different tenancy options for UG vs PG students.
I would start looking now, and write a list of pros and cons for each place, as well as prices, locations and accessibility to town/uni. As you will likely be applying as a single individual, it should be easier to find somewhere later on in the year, compared to groups of people looking to book out a whole apartment/house, so I wouldn't worry too much about running out of time. However, the sooner you start looking, the longer you have to think about it and decide.
Personally, when I was looking at accommodation to start my PG course, I just went and booked the cheapest halls that my uni offered, because I knew I wasn't going to be at home much compared to the amount of time I would spend on campus - I figured I'd only be at home in the evenings so it didn't bother me too much. My flatmates are all UG students but we honestly just keep to ourselves most of the time so there hasn't been any problems!
Hope this helps a little? Good luck!
Jorja (LJMU Student Rep)