Packing clothes for college can often be tricky, as it's hard to differentiate between what you need, and want you want. We'd always recommend having enough items for a week, so you can save time between washes but not have too many items to carry. You should also pack your clothes based on the season in which you are starting college. Most universities start around September time, which means mid-season items are best: a couple of jumpers, jackets, and pieces that are great for layering. You can always return to your parent's home to collect or swap out items you need.
When it comes to packing clothes or any textiles, rolling them tends to be the best way to save space when packing. Use a suitcase and layers your clothes tightly to allow for as much room as possible. You can also use some vacuum-sealed clothes bags like these Amazon Basics Vacuum Compression Storage Bags that come with a hand pump to compress any clothes as small as possible.