How do I know which parts to replace on my drafty front door?

The good news is almost all of this stuff is generic. Door sweeps come in standard widths for 36 inch doors, and the weatherstrip that runs up the side of the frame is sold in rolls or kits that you cut to length with scissors or a utility knife. You don't need to pull the old pieces off and haul them to the store, but do snap a few photos of how the old side strip sits in its groove before you rip it out. Some frames have a kerf, a little slot the strip presses into, and others have the strip stapled or glued to the stop. That changes what kind of replacement you buy, so a photo of the channel is more useful than the old squashed strip itself. If your frame has no groove, you can just nail or stick on V-strip or foam, wich honestly seals better than the factory stuff anyway.

For the sweep, take the door off is overkill for most of them. Most sweeps either slide into a kerf on the bottom of the door or screw on, and you can ussually do the swap with the door hung. Just close the door partway and work underneath. Measure the door width and check wheather your door bottom is flat or has an L shape before you buy.

On the gap at the threshold, look closely at the sill itself. Many aluminum or wood sills have adjustment screws along the top that raise the middle strip, so check that before assuming the seal is dead. If the sill has pulled loose from the slab underneath, a few long masonry screws through it will pin it back down, and a bead of good exterior sealant under the edge stops the draft coming under it. As for order, your instinct is fine but I'd do the side weatherstrip at the same time as the bottom, since it's all one job with the door open and the materials are cheap enough to buy togehter. The main thing is to close the door and check for light and even contact after each fix, because a sweep set too low will drag and chew itself up again in a season.

Seconding the bit about checking the sill screws first. I was convinced my threshold seal was shot a couple winters back, spent an evening prying at it before I noticed the middle strip had sunk down flush on one end. Turned the adjustment screws a few turns with a Phillips driver and the draft mostly vanished without buying anything. Worth doing that check before you order parts, since it might save you a whole shopping trip.

Not sold on the claim that stick-on foam or V-strip beats the factory weatherstrip. I tried that on my old back door one winter and the adhesive let go by spring, left a gummy line down the frame I had to scrape off. Foam also flattens fast where the door presses hardest. The kerf-style replacement, if the groove is there, sits in the same spot the original did and lasts years. The stick-on route is fine as a stopgap but calling it better than the factory stuff is a stretch in my book.

Before you spend a dime, do the dollar bill test we used to run on every cold-call complaint. Shut the door on a bill at a few spots up the latch side. If it slides out easy, the door isn't pulling tight against the stop, and no seal on earth will fix that. Forty years of houses and half the drafty front doors I saw were just sagged on thier hinges. Tightening the top hinge screws, or swapping in a couple of longer ones into the stud, has closed more gaps than any roll of foam I ever bought.

Lurker here, first post so go easy on me. My situation is a bit diffrent, my side door is one of the narrow 30 inch ones and all this talk of standard widths has me second guessing. If the sweeps are made for 36 inch doors, do you just trim the extra off the end, or does cutting mess up how the flap sits? I cut a foam strip too short once doing a window and learned the hard way you can't glue it back on. Also curious how tight the new sweep should sit against the sill, since mine barely touches right now but I don't want it screeching every time we open the door.