I don't know the highest amount of current it can generate. 52 A is the highest I've seen someone mention. IMHO, if you're using a back fed breaker, the safest bet is to use wire to support the rating of that breaker. So, 50A or 60 A are the two logical choices. Making the wiring match the breaker seems logical.
That's ok as long as you are keeping within 50 feet from the generator to the house panel. Once you start going beyond 50' you start incurring a voltage drop and that drop can only be dealt with by going to a larger circular mil wire. And even that might be pushing it in some cases.
On another note: If you are back feeding lets say a dryer plug that is wired with #10/3 or 4 and that run of 10/3 is 40 feet from the dryer back to the house panel. If you used another 50 feet of 10/3 to back feed that dryer plug from the generator now you have a total of 90 feet of 10/3 cable from your emergency generator to the house panel. NOT GOOD.
Even if you fed the panel from the genset to the back feed dryer plug with #2, you still have that 40 feet of #10/3 to contend with in the supply path. Your weak link is that 10/3. You would have to shed loads at the panel by disabling breakers so you do not/cannot exceed the current capacity of that 10/3 wire(which has now become your emergency panel feed).
A 50 amp rated range outlet would be a safer backfeed point and even that has limitations depending on what devices will be drawing off of it from its location back to the panel.
Now, add in the fridge, the well pump, sump pump, AC unit, lights, furnace blower, et al and you can quickly see how the loads tax the feed.
When you are feeding a panel from the street, it is usually fed with adequate sized cable to accommodate total load of the house and usually any additional loads within reason unless its a very old low amperage service to begin with. It is then distributed with appropriate sized wire point to point for each device fed. The dryer takes 10/3, the electric stove takes #8 or #6 depending on the size of the stove, the furnace takes X, the well pump takes X, the sump pump takes X
The whole supply circuit is only as good as its weakest link. The closer you can backfeed the panel and the larger the wire size you can use in any situation, the better off you are.
Back feeding can be done but it must be done with caution as to what the total draw is down the line at the panel. You will have to shed loads so you don't exceed the current capacity of the smallest cable in the feed circuit.