RIGHT!
"Deep Cycle" "Trolling Motor" etc - Starting your Generator is OK with these
Its "Rating" should show "Amp-Hours" not "Cranking Amps"
Try NOT to have "Starting" in its designation since there are "Combination" batteries that really aren't good at either.
If you have space for two batteries, look into a pair of SIX Volt ones that you connect in Series for 12 Volts. A pair of 12 Volt, connected in parallel, just don't seem to "Play Well Together."
We have room for only one battery. We don't boondock, so one battery fills the bill for us very well. I get the 12 Volt Deep Cycle from WalMart. They last me several years because I'm lucky that our OEM Converter/Charger doesn't boil it.
WM's batteries probably are not the very best, but the availability and price made them very desirable for me. If I need a battery, there's almost always a WM nearby and it's probably open 24 Hours.