Yeah that looks like the standard menu. There were a few alternative dashboards that were made to look a bit like stock but that very much does look like the original. Things tend to be launched from the dashboard and most people then use alternative dashboards.
There are two broad classes of original xbox mod
1) Hardmod
2) Softmod
Hardmods are chips and the so called TSOP flash available for the slightly older models.
Softmods are much like they imply, done in a couple of ways (hotswap and hacks launched by bad saves in a game).
There are some extra hardmods like overclocking and more memory but they are of very limited use.
Both do much the same thing, the only thing softmods do not do is allow easy hard drive replacement (you have to find a model that locks and actually lock it --
http://xboxdrives.x-pec.com/?p=list&v_size=500&sort=brand ). Taking it apart would tell you very quickly and there are kind of some software things you can do but nothing like the Wii CIOS reports. When you were told chip I guess it could also have been shorthand like some people use terms like jailbreak today.
Not sure what goes with whatever chip you have but usually it is stuff like "power on using the eject button" if you want to launch hacked modes (unhacked tended to be the only way to get on xbox live). If it is a really old softmod you might have to do something else like go to a certain menu to launch a font based exploit, I hope it is not that though even though it would not be bad to fix.
XBMC is wonderful, however with the scene and most others having now shifted to H264 as a video standard the old xbox (basically a 700MHz p3 with no memory) does choke a bit on it. A raspberry pi with XBMC (I guess it is called kodi these days) will beat it easily. I do suggest it though, it is a bit heavier than other alt dashes but it is still good. The XBMC team dropped support for the original xbox a while back but the xbmc4xbox folks are where you want to be looking these days (
http://www.xbmc4xbox.org.uk/ ).
Video and music will load over network* and USB (the controllers are basically USB devices so you can solder in a USB extension and have a very limited use USB1.1 port). Games will only load off discs and the hard drive. You can try setting book types on the discs but if you have one that struggles to read a type then I say just get the ones it likes, or use the superior hard drive loading. The xbox originally shipped with a 8/10 gig drive, of which you can use about 4 (most xbox games hover around the 2-3 gig mark but you can shrink them a tiny bit, some are dual layer though). The 10 gig drives were formatted as 8 but you can gain an extra 2 for another partition. Obviously you will run of space quite quickly just using the stock hard drive but the chip, if it exists, should allow you to stick any old IDE drive in there. Once you have a nice sized drive in there then you can transfer things across easily enough (basically everything on the xbox uses FTP to manage this so make sure you have a copy of filezilla, users and passes are typically both xbox and the port is usually 21 as well).
http://www.xbins.org/applist.php covers what various pieces of homebrew are out there, xbox homebrew was typically made with the official SDK so you tend to have to download it with xbins (search for a program called auto xbins/easy xbins). Way back when there was a tool called Auto-Installer Deluxe which had all the nice emulators, homebrew and whatever else but the trackers for it went down a while back and it can be harder to find these days, if you can get it though then do.
*XBMC supports basically every protocol that matters, including plain old windows shares, which is nice, especially when it means I have been doing it for many years at this point when other things are sort of thinking about catching up.
I will leave it there for now.
