You could do a ton of things to upgrade things, but that engine will get you around for decades(if it is overall sound right now).
Yes, it is finicky because it is carb'd, unlike all the new fuel injected stuff that is carefree and very easy to drive. You need to give it a moment to warm up when cold and it will be a bit touchy at times until them. Back then it was "normal".
Sounds like the carb might need a simple rebuild. Also sounds like the accel pump is lagging a bit and causing the stumble or stalling. Nothing catastrophic, but again just needs some attention. I really hate those old Autolite 2bbls, but they came on everything back then. If you keep it tuned up properly, it should last a long time.
Yes, you can buy a bolt on fuel injection set up these days. Completely stand alone. Though they are around $1000-2000 and take some skill to install and get running. I wouldn't waste the time.
Here is one option just to show you:https://www.holley.com/products/fuel_systems/fuel_injection/sniper_efi/factory_refurbished_-_sniper_efi/parts/FR550-510?gclid=EAIaIQobChMI79H63OCV5QIVQdbACh1H0QVYEAQYBCABEgK4I_D_BwE
My guess is the transmission needs a few seals(front pump and output shaft) and maybe a pan gasket. Nothing horrible, just need a mechanic with a lift and a few hours.
If you want to replace the engine with something else, you'll need a transmission also since nothing new will bolt to that old C6 that only fits that model engine(360 which is in the "FE" engine line). Nothing else will bolt to your factory frame perches, so if you want a 302 or 351, you'll need perches to fit that truck. Then you can find a fuel injected small block and something like an AOD(cable operated, non electric) and have OD to make long trips easier. I'd likely say you have 3.25 gears out back? Unless someone spec'd something a bit steeper, that was a common gear for that kind of truck.
In all, if the engine runs well overall, have a competent mechanic that still works on carbureted engines do a basic tune up(like carb rebuild, new points, plugs, wires, etc). Finding someone like that is hard to do anymore. Many places won't even talk to you, or may screw it up worse then it is now. Sad, but true.
Watch the exhaust manifolds. Very typical they crack. Sometimes they just erode around the port and leak. Once they start there is no good fix. They don't use a gasket, but some try to use gaskets and they just don't last. The upper bolts in the manifolds will break off if you try to remove them. The holes are open in the back and allow moisture and rust. The lower holes are blind(not open) and come out easily even after all these years.
Here is your truck, right side up. Using a IPad or such will unfortunately rotate pictures for some dumb reason. Typical.
Good luck with it. Looks like a pretty nice truck.
I've had my '69 F100 for 31 yrs now. It came with a 360 also. I replaced that many decades go. It is one of my hot rods.
I'm no expert, but I did stay at a Holiday Inn Express last night.