For the purposes of this discussion there are four types of hack.
Straight DVD mod
Drive emulator
JTAG
RGH
Straight DVD mod and drive emulator can go on live. RGH can be made to go on live but you are looking at some serious annoyance to maintain it and more expense (though not an awful lot) to go on live, it will be unhacked on live though.
Do note that RGH and JTAG are not DVD mods and with on you can not run copied DVDs, this does not bother most though.
Straight DVD mod then.
If you are lucky in the type of sata ports you have on your computer, have some torx bits of the right size and have the right DVD model in your 360 this could cost you nothing but an hour and some high volume swearing (never met someone that had their first DVD mod go cleanly, if by some miracle it goes cleanly then about 15 minutes once you have the DVD drive out).
If not a compatible sata card (usually something in the Via 6421 range) is somewhere between $10 and $20 though you mind find a cheaper one second hand.
After this eh... varies widely really. You might need to buy or build some extra hardware and you might need to buy a replacement board for modding some of the newer slims.
To burn most newer games you will need a special DVD drive, there is a slightly lesser method (you have to set the mode for each burn rather than just burn) and I am not sure of the compatible list right now so probably about the price of a normal DVD burner really. In case you missed it you will need dual layer discs and most will, quite rightly, tell you to go for the nice Verbatim discs.
DVD emulators. Will require the first part of the DVD mod or a JTAG/RGH setup (though why you would have an emulator at this point I have no idea) to get the DVD keys to program the emulator. The emulator seems to run £70 or about $110 USD and up. You will also need a USB drive to stick on top of this.
JTAG. A trip to radioshack for some components there, the ability to solder on modern electronics and a PC with a parallel port. You can buy in something to dodge the need for a parallel port, not sure what the going rate is for that right now but you can also use it for RGH in a moment. As DinohScene said a 7371 or earlier xbox are rare things indeed these days. Also though it is not a certainty there is a good chance said xbox would be one of the older and unreliable as you like models.
RGH. Varies a bit depending upon the actual chip you use though for the older but just as functional type you could possibly still do under 30 USD, the ability to solder modern electronics and the need for two parallel cables and a trip to radioshack. If you would rather not use parallel cables then you can buy things in as well. Price here would probably end up around 70USD if you shopped around a bit and slightly more if you say "screw it, I will just buy it in". I am not sure what others are charging for installation these days but it is typically not an awful lot different here. Some of the newer chips, which might be necessary or make your life easier if you are on newer kernels or have a newer 360, cost a bit more but not a ridiculous amount more.
JTAG and RGH also have the benefit of running from hard drives, USB drives, region free, modded games, XBLA and DLC, homebrew (not that there is much of anything), ability to use any laptop sata drive as a hard drive and more besides.
