Be sure to price batteries before you decide what to do. It takes a bit of work to decide what you need. If you use a 12V battery, that would be 50A for a 600W load. Watch wire size. Going to 24V or 48V makes for lower current and smaller wire, but is expensive.
Batteries should be a deep discharge type (not an automobile starter battery). Bateries should be protected from cold and serious heat. They need to be checked for electrolyte level regularly. They will emit hydrogen and must be vented (if you are using flooded cells). There are gel and ones with the electrolyte absorbed into the separator material. They don't gas but are more touchy about proper charging.
To get long life, the charging and discharging must be appropriate to the battery. Discharging the battery to less than 50% (there are other numbers) will shorten life. The charger should be one that is smart enough to do it right. Outback, Xantrex, and others make inverters with built in chargers.
Figure out how long you want to be able to run the pump before you deplete the battery. Then the 0.6 KW X run hours is 1/2 the capacity of the battery you need. Note that you need to know what the specified KWH for the battery is at your specific current draw. The available total power available decreases as the current draw increases.
A good inverter (Outback and the rest in that class) usually have a pretty good capability to take short term surges (e.g., motor starting). Check the specs. You can if you wish stack two inverters and feed the whole house with 240V (see manufacturers specs). Remember, if you have only 120V from the generator coming into the box, if you connect that to one of the hots and ground, only half your house circuits will be energized. If you try to connect the generator to both hot wires, anything running on 240V won't work. I think that if your house wiring shares neutrals in some cases you could overheat the neutral doing the parallel thing.
You would want to use a real transfer switch. I believe square D makes a mechanical link that lets you use the breakers in the box to switch. Of course the breakers in question need to be in the righ places for it to fit. I would strongly recommend you not attempt to do this by manually opening and closing the breakers individually. This could hurt someone working on the power line if you got it wrong. I suspect code would want a transfer switch. I have not looked at it cause I would not do it without a transfer switch.
Go through your house and figure out what load you would need to have running during a power failure. Maybe you can just connect the generator to the house and pump. You should keep in mind what the load would be if you were managing for a power outage and what might be turned on when the power goes out. With a manual transfer switch you can go to the box and turn off big/unneeded circuits and turn off excess things that were running.
I did some arithmetic in my house and I believe I can run the house on a 5-6KW generator with some load management. My well pump only draws about 500W and does not have the surge on start characteristic of more common pumps.
Don't forget you have to have a place to store fuel. I am going with propane because it is easy to store, clean burning, and does not spoil when stored, and is the most expensive alternative. You can get a conversion kit for gas to propane engine. Propane is particularly good in this application becasue if you don't need it it will still be undeteriorated. And you don't have to keep going out in the rain/snow to add fuel.
I was rather thinking about a battery bank kept on float charge when the power grid was running and go through an inverter when power fails. The transfer switch in the inverter is designed to be grid attached is so fast even you electronics is not likely to see the switch. It is basically a whole house UPS. The problem is that it is very expensive. I could sort of justify it if I had solar collectors, but it is a hard sell just for backup. I would use 2 Outback inverters, get a smart motor starter to run the electric start Honda generator, and work out a charger for when the inverter is running. This may or may not need extra equipment: I have to read the manuals. Doing this would not use the generator to directly supply power to any load. It all goes through the battery bank.