Though the Basic Economy fare rules differ from airline to airline (and always read them before you book), most allow only a small personal item to be carried on. None allows you the option to select your seat when you buy the ticket, and only American gives the option to do it at all, 48 hours before check-in, for a fee. All Basic Economy fares place you in the final boarding group, though again with American, elite members keep their priority boarding.
All airlines allow you to check a bag for a fee, but if you show up at the gate with a large carry-on, they not only charge you the $20-25 checked bag fee to put it on the plane, they also charge a “service fee” of up to $35.
Essentially, the old “I’ll just check it at the gate” hack doesn’t work if you’re flying Basic Economy. Your best move here is to just check your bag for the usual fee (elite members and credit card holders still get this waived on airlines where it’s applicable) and stick with your laptop bag as a carry-on.