One necessity is a jack. This is the standard Ford screw jack that was issued with every car
until 1925, when it was replaced by a pressed steel version. Some people dislike this jack,
but I've found it perfectly adequate. Along with the jack, it's good to have wheel chocks to be sure the car doesn't roll, and at least one 2 x 8 or 2 x 6 block to put under the jack. Sometimes two blocks are better than one.

If you carry a spare front wheel you will need
the #1349 Ford wrench...

...and if you carry a spare rear wheel you'll need a wheel puller, a socket to fit the wheel nut,
a breaker bar to get it  good and tight, pliers, and cotter pins

If you have demountable
rims, a Ford #2335 wrench
is good for the lug nuts. It's also used for spark plugs and head bolts.

My opinion of Ford's little tire irons is that they make changing a clincher tire the job from Hell. I consider them suitable for display only.

I carry three of these inexpensive 24" irons from Harbor Freight, more than twice the length of the Ford irons. They exert plenty of leverage to stretch a clincher tire onto the rim.
This is not intended to be advertising. I'm just showing what works well for me.

On the recommendation of a fellow Model T aficionado who has been in the game for many years,
I bought this bicycle foot pump. I used it successfully — once.

The next time I had a flat and tried to use the foot pump it wouldn't get much above 40 psi, which is woefully inadequate for clincher tires. Several passers-by stopped to see if they could help. The man on the left had a battery-operated pump which might be OK for mower tires, but lacked the guts for clincher pressure. The other fellow lived nearby, and fetched a tank with enough air in it to do the job.

For a Model T with six volts or no battery at all, a modern twelve volt compressor obviously is not a choice. But before catalytic converters came on the scene you could get a pump that screws into a spark plug hole and is operated by engine compression to pump ambient air (not fuel mixture from the engine). In fact these pumps are still sold for motorcycle use, and vintage models like this can sometimes be found on eBay. To use one of these you would have to make an adapter for it to fit a Model T plug hole.

Another air source that requires no electricity is the same one that was used a hundred years ago. I was pleasantly surprised to find that I could pump a clincher up to 72 psi with this.

The secret to using an original pump or a reproduction is in the connector. A modern connector has a center post that depresses the pin in a tire's Schrader valve and holds it open. This is no good, because the old pump has no check valve. If you have a modern connector on the old pump and screw it onto the valve stem, air from the tire blows into the pump and raises the handle like an old time hydraulic shop lift, but a lot faster. Every stroke you make with the pump pushing air into the tire is met by the same air coming right back out. I solved this by using a small grinder to remove the center pin. That lets the Schrader valve in the tube stem act as a check valve. The air the pump pushes in stays in. If you have an old pump that lacks a check valve and has a mistakenly-installed modern connector, you can buy an old style pinless connector (Lang's Part #2338CS) or you can remove the center post as I did on this one. I used a small grinder, but a better way would be to remove the valve from an old junk valve stem and screw the stem into the connector as a guide to drill out the post without damaging the threads. Just be careful not to drill too far.

Nowadays these are usually plastic, but you can still find the old style metal stem caps. Either one is good to use as a backup in case the Schrader valve inside the stem develops a leak.

The stem valve is one car part that's about the same today as it was a hundred years ago. You won't need it often, but when you do you really do, so it's good to carry a few spares.

Not every valve wrench is as elaborate as this one, and it doesn't have to be. All it has to do is remove or install a valve in the stem.

This stem cap doubles as a valve wrench if you need one. It's on a spare stem that serves as a handle.
A dab of Loctite can keep them together.

So let's say you deal successfully with changing your tire or tube and you drive on to the next town and go to a tire shop to have your flat repaired. That may happen, or you may be told (as I was), "Nobody does tubes anymore."  You may be lucky enough to find a real tire shop in the same town, as I was, and they will fix your flat. But in case you don't find such a place, it's a good idea to carry a patch kit containing a couple of tubes of rubber cement, and several patches. Most patch kits include something to rough up the surface before you apply the rubber cement, but if yours doesn't you can include some coarse sandpaper.

Talcum powder is a good lubricant to help a tire slide onto a rim.
A pill bottle will hold enough to do several tire changes.

Murphy's law, and fate in its infinite whimsy, may decide that you should enjoy some unscheduled pneumatic entertainment far from any help, perhaps even beyond cell phone range, so it's wise to be prepared.