A heat treating oven is little more than a well insulated and reflective chamber (that can hold AND withstand heat treating temps), with a CONTROLLABLE heating element (again, that can hold and withstand HT temps).
The variables that come into play are chamber material (aka refractory), element type (as well as how it will be powered), and controller (PID).
Grade 23 (good to 2300F) fire brick is probably one of the more common oven/kiln materials. It will be stable at the common temperatures needed for heat treating knives, and it will hold and reflect more heat than a grade 26 or higher.
Kathal or NiChrome wire makes a good element.
As for controllers? There's cheap ones and expensive ones. Some of it depends on if you want programmable functions, ramping/soaking capabilities, etc...
www.auberins.com is a good source for decent PIDs, and the various accessories you need to make them work (Relays, heat sings, thermocouples, etc...)
Now, as for the forge vs. HT oven/kiln question:
A Heat Treat oven is typically a little more precise and controllable than a forge. If your main goal is heat treating, I'd probably opt for the oven over the forge.
As for the 120V oven, it can be done, but it will take a lot longer to come to temp than a 240V oven. If you could make either work, go with 240 and maybe a 3000W element.
Another option you might look into is the "knife dogs" oven at USAKnifemaker.com. IIRC, they start at about $650 to $700 for a basic model.
If you do plan on building one, remember this: The bigger the chamber, the longer it takes to heat, and the harder it is to maintain a steady temp. a 4x6x18 opening is usually pretty adequate, and easy to heat.