How to upgrade an iphone se to an iphone 6 or 7?

Can i just buy the new phone and then transfer my sim and stuff oer or does it take more? How can this be done?

You would probably want to upload your contacts to iCloud first.
Some things on if it is wise may depend on if your SE is already paid off and if you have exceeded your trial period because if you have only had the SE a few days you might be able to upgrade through your phone company likely with a restocking fee for the SE.
That is you should be able to put the SIM in the new phone if you have AT&T or T-Mobile.
You phone company website might have instructions and a list to tell you if the phone is compatible.

Yea you could buy the phone & transfer your SIM & content via a backup. That's about it.

It's easy. Just do the iCloud backup on your current iPhone.
Switch the SIM to the new one.
Do the iCloud restore to the new one, and that's it.