I fear I'm not dead certain on the size, but looks like a YUASA YTX-12BS would be correct.
I'd search a bit and make sure of that, or just check the old battery, the "12BS" part should be consistent for the size.
Some folks recommend checking the dimensions then finding whatever has the highest CCA rating (Cold Cranking Amp) available
I generally go with the recommended, but anything that fits would work of course, they're all 12v.
You can buy batteries pre-filled, or not. As noted before I choose "or not" since I know the battery will be fresh then
You can buy from any number of outfits, but I stick with YUASA, generally buy from them via Amazon https://www.amazon.com/Yuasa-YUAM3RH2S-YTX12-BS-Battery/dp/B000WK4CS4
is the linjk for that.
Filling 'em isn't a big deal, just read the instructions first, then follow them.
You will need a trickle charger to give it the initial charge (I have a two amp setting on my jump box that I use for this)
Regardless of what you go with I do recommend you go with an AGM (Absorbed Glass Mat) battery, & while installing it remember to add on a pigtail for your trickle charger/battery tender for when ya park this for more than a couple days.