In your opinion, what type/s of battery would one typically choose for storage?
There's three options that I'd consider depending on application.
LiFePO4 (lithium iron phosphate) = the current "state of the art" way to do it and "on paper" has a lot of advantages. It's a less proven technology, relatively new versus the others which have been around for ages, but can also be discharged a lot more heavily without damage when compared to lead acid. If $ isn't a consideration then LiFePO4 all the way....
Gel (lead acid) = old tech but a very "set and forget" option that doesn't really need maintenance. Main advantage over LiFePO4 is the very proven, predictable nature of them. They're heavy and so on yes, but they just work without much fuss. If it must work, and you're risk averse, then Gel is your friend.
Flooded (lead acid) = old tech, high maintenance and best avoided by anyone not keen on tinkering with things. But that said,
if they're properly maintained then they'll last a very long time and can end up being the cheapest option. A lot of hobbyist / tinkering types love them for this reason. They're reliable as such, and cheap - as long as you don't mind having to keep them topped up regularly. They're definitely not a "set and forget" option and not well suited to being regularly moved around either (unless permanently mounted in a vehicle etc).
Stand alone household on solar = LiFePO4 would be the "modern" way but also the least certain in terms of lifespan. Gel or flooded lead acid are less risky financially in that sense, you can be fairly confident of their lifespan, although they're inferior as such.
Backup to mains = Gel or AGM would be the easy option. Or you could use LiFePO4 if you're keen.
Gel and AGM (Absorbed Glass Matt) are both variants on the same thing - a sealed lead acid battery. Gel is somewhat more durable but has a slower discharge / recharge rate than AGM. Hence the use of AGM in things like computer UPS' with a small battery designed to last 15 minutes while you shut things down etc. AGM handles such a rapid discharge better than Gel does. But if you were going to size the battery to keep the system running for hours then there's no such advantage - and in that case the longer lifespan of Gel wins out.
There are also other battery technologies, eg NiFe (Nickel Iron) but you're not likely to consider those for home use. They do have some applications however, and the primary benefit of NiFe is their very long lifespan - we're talking 25 years or so. Downside = expensive and inefficient. But they're extremely robust which is the good point.
Something that cuts across all of this is the type of battery itself. An SLI (Starting, Lighting, Ignition) battery (commonly known as a "car battery") won't last long if deeply discharged. It will work yes, but a car (or truck etc) battery will have a short lifespan if it's being deeply discharged on a regular basis. It's designed to provide a huge current for a few seconds to start the engine, then be immediately recharged. It won't like running your computer all day. In contrast, a proper deep cycle battery is the opposite - it physically can't produce the high current that a SLI battery can, but it will survive many, many more discharge and recharge cycles in a solar or backup power application.
So Deep Cycle is what you want in any application for backup power, solar etc.
There are also such things as "marine" batteries and various other things. Typically, they're a hybrid - designed to be sort-of deep cycle but still put out a lot of current to start an engine. Leave them where the name implies, on boats, and stick to proper deep cycle batteries for solar etc applications.