Welcome! The Amiga can be a challenge to get into (difficult availability of parts), but it's a lot of fun. I think you'll come to love the AmigaDOS command line, and ARexx for inter-process communication.
First order of business to ensure the longevity of your system to to make sure the battery isn't leaking. The clock batteries Commodore used were not designed to be around this long, so they usually leak and can easily damage the motherboard. In the A2000, the battery is located under the drive chassis. The Amiga only needs the battery to keep time while switched off, so the system will still work if you can't replace it right away (or ever). You can either cut it (carefully) from the component side of the board, or desolder it from the bottom.
As tone007 (EDIT: and AmigaED) says, those are not standard PC keyboard and mouse ports. In addition to the keyboard adapter, you can also get a mouse adapter that lets you use standard PS/2 mice.
If you're having trouble finding an Amiga monitor, you may want to look into the Indivision ECS, which will let you use standard VGA monitors.
Again, welcome!
