I just spent about 45 minutes typing a reply and the doggone forum machine ate it...I am not a happy camper!
The bottom line, since I'm not willing to retype everything I wrote is that a 'starting' or 'cranking' battery is the worst thing you can put in a system that's designed to take a long-term load. They have many thin, fragile plates designed to increase the surface area for optimum production of "immediate need" power (like for a starter) and they're meant to be charged right away and quickly. A deep cycle battery has fewer but much thicker plates to handle the chemical process over a long period of time as it works towards the center of the plates. That's also why a deep cycle battery needs a long slow charge; so that the chemical conversion can work in reverse back to the center of the plates.
Every battery sheds plate material during the conversion process from sponge lead and lead dioxide to lead sulphate and back again; deep cycle batteries with their thicker plates are designed to withstand this for many hundreds or thousands of cycles. A thin plate starting battery is often a goner after leaving the car lights on a few times; the plates are literally broken.
Sulphation is what happens to a discharged battery. Lead sulphate forms in the plates during discharge; if the battery isn't charged right away while the lead sulphate is still soft it will harden and it will be difficult or impossible to recharge the battery...it's then sulphated.
When a wet cell battery is overcharged it gasses; eventually this will lead to drying out the plates and failure. Overcharging also sets up a galvanic reaction in the postive plate grids and will literally destroy them. If you're going to leave your batteries on a charger it should be a good one!
You should have as much battery power as you can logically handle (think about your charging capabilites too) for inverter use. It all comes down to percentages; the higher percentage of the battery the load is, the faster (in an accelerating manner) the battery goes dead. Amp-hours are generally rated for a continuous 20-hour load; a 100 amp-hour battery can handle a 5-amp load for 20 hours. If you increase that to 10-amps you'll only get 84 amp-hours out of the battery, or 8.4 hours of use (not the 10 you might have anticipated). A good rule-of-thumb for inverters is you want 20% as many amp-hours than the inverter has watts; i.e.- a 1000 watt inverter should have at least a 200 amp-hour bank to work from.
For longest battery life you don't want to go below 50% charge on your batteries; when you do you start to damage the plates beyond just normal ageing. A battery is 50% discharged at 12.2 volts (and fully charged at 12.6); that's a far cry above the 10.5 volts where a battery is considered "dead'. Constantly taking a battery below 12.2 volts will *significantly* shorten it's life (that's money!).
I think I got most of what I was trying to say in here; it can be a complex subject but one most of us are really interested in. Offshore sailboats have dealt with these issues forever; info on them is easier to come by than bus stuff! One of the best books out there is Nigel Calder's "Boat Owner's Mechanical and Electrical Manual". There's also a lot of info on the web; particularly on solar power and alternative energy sites.
Hope this helps...