It sounds like you have limited funding (most of us do) and are looking at an $11,000 bill for all this stuff so far. Residential electrical work is not to be trifled with. But it is not too complicated, and you do have time to learn. You might consider doing the bulk of it yourself.
You'd need to school up, though. Google won't cut it, it only answers questions and you need a well-rounded grasp to know what questions to ask. I would go to the library and look at books on electrical work. Find one that feels accessible, and read it cover to cover. And then, read another one.
You don't need every fine detail - for instance you need to know the fact that when trenching, different wiring methods require different burial depths. But you don't need to know what the depths are, Google can tell you that. Google won't mention anything else, like that you need to throw a ground wire into the trench! That's where the book knowledge is vital.
I once rewired a 20,000 square foot factory building for under $1000. Good chance that would pay for the components of a multi-panel system as I envision here. If I were blessed with an $11,000 electrical budget for a residence, I would spend almost all of it on a large solar/battery system.
Realistic loads for a generator
You've given us the watt numbers from 3 generators, so you're familiar with the unit. Now it's time to look at the nameplate of each of the appliances you aim to power. Most of them will have "watt" or "VA" ratings. The difference is this: an appliance that is 1600 watts and 2000 VA needs 2000 watts from the generator. So VA is the more important number when figuring out how much generator you need.
If you can't find watts or VA, it'll state Volts and Amps: multiply them to get VA. (VA = Volts*Amps, hence the name).
Here, you will find some sobering realities. You will probably find the range is on the order of 7500-9500 watts, way too big for the larger generator. However that is with heavy use, you may get away with one burner.
You will surely find the water heater takes 5500 watts. We can jumper it to take 1375 watts by moving its white wire from the breaker to the neutral bar, but at the cost of taking 4 times as long to warm up water. Several hours worth of gasoline, yikes!
Anyway, you'll need to think about what you can realistically power with these generators. Motors are especially challenging, because they can take 3 times their nameplate VA to start up.
I would feed the small generator strictly through extension cords, and wire the larger one into the panel. Definitely never wire it so there's any possiblity of both gens feeding the panel at once, they will Fight!
The larger generator, I would cable that straight into the old main panel, for now, using its main supply lugs. I want to convince you to be offended by the very idea of backfeeding a panel. Suicide cords, breaker sequence lists, all that is for the birds. This kills linemen. But more immediately, if an inspector sees you doing it, it will draw their wrath! It is so easy to do it right, just do it right.
Both your generators need 12 AWG wire/cable. Given the distance, you would want to upsize to 10AWG, which will ease voltage loss for 120V loads over 10 amps/1200VA.
Your old panel will have 3 fat wires coming in from the service, two hots and a neutral. Remove all three and wrap their wire ends with tape to insulate. The line from your generator needs to go to the two "hot" lugs you just removed the fat wire from. Look at the lug, or the panel instructions, and it will tell you the smallest wire it can safely take. If your wire is too small, use a 200-400mm pigtail of #6 THHN wire which should fit on the lug and also splice to the generator lead with a wire nut.
The ground wire from the generator goes where all the grounds in your panel go. Neutral is tricky. You can chance putting generator neutral on the neutral bar if all neutrals and grounds are already separated. However, if your house has any ground faults, it will trip the GFCI on the generator. Safer is to not use the neutral bus, and simply wire-nut the generator neutral to the neutral wires of the circuits you want to power up.
I don't think you will need a permit if you are obviously doing this for temporary wiring.
The final wiring layout
Wanting a generator changes the landscape. You don't want to get stuck with one of those shoddy, overpriced Reliance style transfer switches that have 6-10 circuit switches to switch between utility and generator one at a time, why would you ever want to do that? Their complexity is useless.
Instead, we'll place all the circuits you want powered by generator onto an subpanel and switch the whole subpanel. This is simply and cheaply done: it has two main breakers instead of one. Something like this one, and look at the price! Much more sensible. And this is quality equipment. The panel features an interlock so only one main breaker can be on at a time. One goes to your main panel, the other to the generator. This one is 60A but you can get larger easily enough.
This generator subpanel could be installed next week, frankly, and would be the permanent solution.
Separate from that, replace the main panel at your leisure. A breaker in the main panel will supply power to the subpanel.