Lithium ion is what you'll need. We (I) lazily call all of them "lithium" when I mean lithium ion. You can't usually charge a lithium battery but you can a lithium ion battery.
Source:
http://www.greenbatteries.com/li-ion...0dif%20Lithium
Lithium ion batteries are sensitive to charging voltage (more sensitive than an AGM battery), if your charging circuit is functioning correctly you'll be ok. If it was me I'd probably buy some kind of charge monitoring device (sparkbright if you want to support UK economy, ebay for a cheaper version).