What kind of siding and install type is this

T-111 is pretty much the standard for that kind of stuff. What kind of a look are you going for? You could always sheath it with OSB and put anything you want on top of that (vinyl, clapboard, etc.)

The 8" Home Depot siding will be too narrow. It's 8" nominal, the actual exposure width will end up under 7". To avoid the need to exactly match widths, consider replacing the boards full height, then you have no butt joints in the siding.

If you don't want to spend for the extra material, finding siding that exactly matches width may not be that easy. You could get someone to mill boards to a custom width. Since you boards have no special exposed profile, someone with a table saw could easily cut boards to match what you have. The raw material would just be nominal 1x12 and 1x10 lumber with one face resawn, which is a pretty common siding raw material.

This is a relatively easy DIY project, but it may take more than 3 hours. Be sure the siding nails you use are either hot dipped galvanized or stainless steel. Electro-plated galvanized nails will still rust. Siding nails have more of a head than finishing nails, so the boards are held tight and can't warp, but smaller than regular nails so the exposed head is not too objectionable.