Lucky you! Of course, the case might look brand new, but the motherboard won't be. It might be in a modern replacement case. What information did the seller provide? The cases were originally bright white, not cream or yellow. Is it white now? You should immediately unscrew it and replace the battery which may be leaking. I've recently been looking at my A1200 motherboard a lot, but I don't remember seeing any battery, though. You should also have all the capacitors changed, but you might prefer to wait until one of them blows because you'd probably have to send your "new" Amiga away to have that done. This may mean being without it for a few weeks.
As for what kind of monitor to use, back in the day I used a C1084S monitor, until eventually either the red, green, or blue component blew out, then due to the price of repairs, or even to get someone to just look at it, I had to get someone to make up a custom lead to use my Amiga with another, older monitor, then I just abandoned my 1084S monitor. AFAIK, they were actually made by Philips, a rebadged version of an 8833 monitor, which was used for various other computers. I think the 1902 monitor was actually made by Commodore, though. As for connecting to a TV using the composite video port, this won't provide the best signal. I use a custom lead of a type widely available which connects the 23 pin D shaped RGB port to the SCART/Peritel connector on a small LCD TV. This type of TV also fixes all the flicker problems I used to get on my old CRT monitors. There has been some debate about if it displays movement in games properly, but I think it's fine. As you're in the USA, you probably won't be able to get hold of a SCART/Peritel TV. There are a few for sale on ebay.com , though. In that case, you should check all the connectors on your CRT TV to see if there's anything better which you could connect to from your RGB port. If not, then try to find an LCD TV which has a better alternative. You can't just run a cable from the Amiga to an HDMI port on a modern TV, though. This requires some kind of adapter fitted internally. There's one which includes a Raspberry Pi, and I think there are some others.
