I don't know any sites that are still specialising in Xbox modding today, most of the ones from back in the day are long since gone.
You can softmod mod an original Xbox without even opening it, however you probably will want to upgrade the small hard drive the Xbox comes with, which is also possible with a softmod.
The Xbox is basically a PC, so it's nothing that obscure once you get it opened.
Some modchips did allow extra things like an LCD screen to be installed in the case and for you to add a couple of USB ports to the front of the console.
Here is a photo i took almost 10 years ago of my modded Xbox with an X3 Modchip installed, the front of the Xbox part of the case has been replace with an aftermarket one from Team Xecuter, this has controls for the modchip, along with a cutout for the LCD screen you see, in addition to 2x USB ports which are wired to controller ports 3 and 4:
It depends what your going for, all i'd really say you need these days is to upgrade the hard drive, anything else has little benefit besides "looking fancy" when playing videos in XBMC.
Back in the day some company did do a processor and ram upgrade for the Xbox, however you'd really struggle to find this today. I believe it was called the FriendTech DreamX if I remember correctly. It wouldn't really say that's essential to get the most out the Xbox though.
I'd advise you decide what you actually want to mod on your Xbox Classic and go from there. Upgrading the hard drive is the most worthwhile thing you can do, along with region changing the console to NTSC if its a PAL console, this unlocks 480p, 720p and 1080i, however that's basically a case of loading a homebrew app once the console is modded.
You might well find someone on a forum or Reddit still offering modding services, however now Xbox-Scene is long gone i can't think of anyone to personally recommend.