Wire floor cages are fine for some rabbits as long as he has adequate resting surfaces, so whether or not you decide to get a solid-floor cage, you should give him something t stand on! Somewhere cushy to lay will make him comfortable as well. Make sure to check that his feet are covered in a full layer of thick fur. Any bald spots on the bottoms of a rabbit's feet means that the wire floor is too harsh and they need to be taken out of the wire floor cage right away. Some rabbits do very well on wire because the fur on the bottoms of their feet is good and thick. That depends on breed (the Dutch is a breed that typically has well-furred feet, so they tend to do well on wire). It depends on your rabbit's behavior/personality as well, though. Provided with resting surfaces, some rabbits will constantly stand on the wire and cause their feet to get worn, so they shouldn't be on wire. Here is an article about the misconception that wire-bottom cages are always bad:
http://shinysatins.weebly.com/wire-floors.html
The basics of rabbit care are mainly to keep your bunny out of the heat, provide plenty of hay (timothy hay or orchard grass for adults, though alfalfa is fine for babies), and plain rabbit pellets (not the gourmet mix stuff, which isn't very good for rabbits).
He looks like a Dutch judging by the length of his face and ears (and markings). He also looks young based on how pinchy his nose is (males usually get more rounded, masculine faces as they get older).
Maybe it's just the quality of the picture, but it kind of looks like he wasn't too well cared for. Young rabbits typically have better fur. I don't know what's going on with the little indent in his fur below his eye. It looks like a molt line, but a two month old Dutch rabbit shouldn't have that. Was he living with other rabbits, in cramped or dirty conditions, or eating anything other than hay and pellets?
Good luck with your new bun!