Having just traded a car for about a 2500watt gennie and cash I have been thinking about the same thing somewhat.
Would it not be easier in the long run to just forget the 120V battery bank and charge a very large 12V bank at high amps instead? OR since you plan to change the battery you draw from with the inverter, charge several 12V banks?
I keep losing the links or/and on the wrong computers at various places, but there is a simple diagram on this site that shows using a non-polorized capacitor to limit the amps of 120Vac and then rectify that with a bridge rectifier to charge batteries. It is said the battery bank will limit the volts up to full charge BUT then DC voltage will continue to climb destroying the batteries as there is no way to limit the volts from this simple AC-dc conversion. It should be safe if you watch the banks voltage though and versital for any bank voltage.
So if I have this correct,
I do not recall how many amps you get through the caps off hand, 1 amp for so many UF. Using the correct UF value of capacitors then you would limit the AC amps down to 25 (far less really) and run that through the bridge rectifier for 25amps at 120Vdc? The 12V battery bank will then hold the Volts down to it's own level while taking a charge, so I geuss here that would be like around 10V for a dead bank and gradually rise as the bank charges to full at around 12.5v or so. But then there is nothing to stop this charger from continuing to rise to 18V, 24V, up to full 120V or higher and anything over full charge volts for your battery bank is going to destroy batteries. So this is a setup you WILL have to monitor.
Now 120V at 25amps is 3000 watts divide that by 12V and you have 250amp charging?
Kinda alot more than I would want!!
Not sure if that is correct way to figure it, I think it is. Having one of those slow brain nights here tonight. So If I figure that correct you would want far less than 25amps comming through the capacitors on the AC side unless you have a very large amp bank. Say if you wanted to charge the bank at around 50 amps DC? I do want about that for mine so, 50amps X 12Vdc is 600watts, divide by 120V and I need about 5amps in caps on the AC side of the rectifier. 100amp DC charging (1200watts) then I would still only need 10amps on the AC side.
As for wire. Looks to me like it's low amps on the AC side here so about anything should work like a decent extension cord, light cord, etc... If you go for higher amps then a cord from an old toaster or electric heater maybe. For the DC side it depends how many amps you want to push, 50amps ain't alot and my comercail 40amp charger has a pretty small cable on the DC side itself. I would say a normal battery cable would be what I would use, grab one from a junk yard for a couple bucks and use the starter cable, should handle about anything you throw at it through the charger with in reason and probably alot more than you need, but cheap 
I buy them for about a buck or two depending on scrap copper value at the time.
Could cut a section of jumper cable also if you have an old set, I buy those also, and then I have the clamp already on the wire to connect the charger to batteries
The charger can be right at the batteries so a long run is not needed for the DC side, and AC side should not have to be any heavier than a normal extension cord rated for that many amps or more, so about any 15amp extension cord 10' long should work fine. Or use a short wire on the charger and plug into an extension cord for the 10' distance is what I will probably do myself then I can use the cord for other things if I want also.
There are times when something like this may be good, for the remote house I rent sometimes this will work nice. Run gennie a little for heavier loads of around 1500watts and dump 600watts into my batteries at same time for latter use. Remember though, the more load on the gennie the more fuel you'll use to run it also. So I use less fuel at 1500watts for just the heavy load or a bit more feul at 2100watts and also charge low batts. For me of course I consider this worthwhile if I need to run the genny at all, I will have battery power anytime I need it without runing the gennie for small loads.
Now I have a 5,000 watt inverter BUT I don't have the batteries to power it at full load. My setup will run my lathe but the batteries aren't putting out enough amps fast enough, are weak, or something because the inverter beeps for a low battery warning while the lathe runs.
1500 watts is 125amps at 12V. So while I make coffee with the genny I will dump 50amps into the batteries for that 10-20 minutes, run the lathe on the genny 20 minutes, 50 amps to batteries again. I will only rarely need to do this anyway.
Now since I would be using this in the manner described, I will probably build 3 of the cap/rectifier chargers and wire my batteries so that I have 3 banks that can be charged seperatly as needed. Use my large 5K inverter on one large bank for heavy stuff, smaller 400watt inverter for lights/tv/vcr/dvd/stero/etc... and this way I can look at the bank voltage and decide if I want to turn on the charger or not for each bank when I run the gennie, and also depending on the load I have on the gennie I can decide how many chargers I can run at once. 2500watts for my gennie means I could run 3 50amp/600watt chargers for 1800watts plus a 900watt load, or 1200watt load and only 2 chargers for 1200watts/100amps 12V dc.
Another thing is I see no reason the output of each charger canot be parraleled, I mean they can be just fine. So Say if I wanted to charge the largest bank only at 100 or 150 amps I could then connect the chargers all to one bank and turn them on, adding up the amps that banks getting at once. So it is flexable in that way also by building 3 50amp chargers instead of 1 charger of 150amps alone.
Now another reason I do things a little different like this myself is I have 4 different types/sizes of batteries so I do not wire all mine into one bank. L16P is a 6v 360 amp hour battery, I have something a little smaller but near same size also, T105 is 200 amphr 6v battery, and 3 115amp 12v also. Except for the 12V ones they are all about $5 or less batteries I bought from a scrap yard and pulse charged and they work fine. SO I wire similar batteries into seperate 12V banks, keeping T105 together and L16p seperate for instance. Then not owning the house I can't put up a windgennie either, so one bank sometimes two has to be hauled to another location for charging then I dump them back to the ones at the permanant at the house as needed. Kinda a pain but keeps me off grid at that house
I use other ways to charge also. Now that I will have a 2500watt gennie in the woods and these cap/rectifier chargers life will be easier a bit. I also am working on alcohol feul, so you know what I will be running my gennie on
I am sure (and hope) some-one will be along and point out any errors or mistakes I might have made about the above charger setup and perhaps give more info on such too.
Now as I keep saying, you HAVE to watch that type of charger to prevent serious over charging. Using on a genny that only runs ocasionally like I will do it is not that big a deal (for me anyway) but a connection to grid power would really need watched close. I have thought about that also and figure a relay or such could be added to the battery side to monitor the DC volts, turning it on at say 11V and off at around 12.5V but I have not done that yet. Perhaps some-one could provide info on that also.
