A simplified overview for you:
Basically there are two types of Lead Acid batteries (along with 3 sub categories);
The two main types are Starting (cranking), and Deep Cycle (marine/golf cart).
Starting
The starting battery (SLI starting lights ignition) is designed to deliver quick bursts of energy (such as starting engines) and therefore has a greater plate count. The plates are thinner and have somewhat different material composition. The deep cycle battery has less instant energy, but greater long-term energy delivery. Starting batteries are the ones we use in cars. They're not suitable for UPS's..
Deep Cycle
Deep cycle batteries have thicker plates and can survive a number of discharge cycles. Starting batteries should not be used for deep cycle applications because the thinner plates are more prone to warping and pitting when discharged. The so-called Dual Purpose Battery is a compromise between the two types of batteries, though it is better to be more specific if possible.
For storage purposes, you want deep cycle.
Wet Cell (flooded), Gel Cell, and Absorbed Glass Mat (AGM) are various versions of lead acid battery.
Wet
The Wet cell comes in two styles; Serviceable and Maintenance free.
Both are filled with electrolyte and are basically the same. Wet cell batteries need to be topped up with distilled water, and are less safe than the sealed ones. They're not sealed, and are "wet" batteries.
Sealed Lead Acid
Gel Cell and the AGM batteries use a gel instead of liquid inside, and are typically sealed. common names are "sealed regulated valve", "dry cell", "non spillable", and "Valve Regulated Lead Acid" batteries. In most cases AGM batteries will give greater life span and greater cycle life than a wet cell battery. These are all referred to as SLA (Sealed Lead Acid)
AGM: The Absorbed Glass Matt construction allows the electrolyte to be suspended in close proximity with the plates active material. In theory, this enhances both the discharge and recharge efficiency. Common manufacturer applications include high performance engine starting, power sports, deep cycle, solar and storage battery.
Typical lifespan of an AGM @ 40% DoD is about 300 cycles.
GEL: The Gel Cell is similar to the AGM style because the electrolyte is suspended, but different because technically the AGM battery is still considered to be a wet cell. The electrolyte in a Gel Cell has a silica additive that causes it to set up or stiffen. The recharge voltage on this type of cell is lower than the other styles of lead acid battery. This is probably the most sensitive cell in terms of adverse reactions to over-voltage charging. Gel Batteries are best used in VERY DEEP cycle application and may last a bit longer in hot weather applications. If the incorrect battery charger is used on a Gel Cell battery poor performance and premature failure is certain.
Lead Crystal is a newish variant of AGM/Gel battery that offers better cycle time, but isn't very good under load (high voltage droop).
Its proably the best choice right now if you want to go Lead Acid.
The charger you use needs to be appropriate for the battery type in use, otherwise its going to fail faster.
Charging Lead Acid is more of an art than a science. Lead Acid also has fairly crap capacity / weight ratios, and cost ratios.
My opinion is that Lithium (LiFePO or its sulphur variants) will wipe out Lead Acid in a fairly short period, as the pricing for Lithium is cost effective - its already dropped to similar levels as Lead Acid pricewise, and it gives far more capacity.
I forecast that in 3-5 years Lead Acid will be uncompetitive to Lithium.
Lithium doesn't need tweaked charging tech - its basically charge till you get to a specific voltage, then stop. It also can supply high currents without voltage droop. Lastly, it's also far safer.
Back to now though, stick to the same chemistry type you currently have in the UPS, as the charge circuit (should be) optimized for that Lead Acid battery type.