For the most part this was the last gasp for tie in/cash in games, and while Marvel was on something of a roll it had not yet become what it eventually morphed into, and many treated them accordingly and just had rushed cash in type things. To that end you might be harder pressed to find that many that played them, especially around here.
I am not going to say 360 spiderman does not have its fans but you are not going to see the same kind of fondness for them like you will for the PS1 and PS2 efforts (the web swinging sections were a lot of people's zone out and relax type game), or the more recent PS4 exclusive one.
I mostly played them round friends when I did. In general I will not be adding them to my 360 collection, even if I see them for £1 each in a charity shop or something. In general I don't care to play as a character from something else (same universe is a different matter) but if it is your thing then you might be more forgiving. Price wise they also seem pretty high in some places I was searching for this, though I don't know if that is a sign of the times (360 games, consoles and the like have been creeping up in price this last year or three). If you are doing alt versions as well then do check out what happens for the various consoles they might be on -- some of the handheld stuff did pretty well (if they did not much care what happened for the console editions they certainly did not for the handhelds, and occasionally letting programmers run free does make for interesting results) and was rather different.
On the flip side if you never played the PS1 and PS2 efforts (both of which I imagine have not aged the best) and rinsed those I could see you having a pretty good time here with something like The Amazing Spider-Man, if not a very challenging one (at which point you would be pointed towards the Batman Arkham games, especially if DC is more your thing). If you are going to do The Amazing Spider-Man 2, most people generally noting it as a lazy sequel to a promising game, then maybe consider the xbone or PS4 version if you can as the 360 was rather long in the tooth by this point and the port/version not the best (not sure what any title updates might do for you).
The standalone games (Edge of Time and Shattered Dimensions) were theoretically supposed to be for fans of the comics (I only ever watched the TV shows/cartoons and they barely touched upon anything covered here) but usually fell flat. That said if you liked the Ultimate Alliance games you might like Shattered Dimensions.
Spider-Man: Friend or Foe is what it is.
Spider-Man: Web of Shadows... minimum viable product for an open world spiderman game is probably how I would describe that one.
Don't think he was in any Lego games around then, certainly not any ones based on him. They can be fun though.
So yeah mostly what would be known as rental games in my youth.