I've worked on a computer desk for years. It's not ideal, but for me anyway, it hasn't been limiting enough to switch.
If possible, it's nice to have two separate areas: a "clean" place with scope, power supplies, meters, a breadboard, etc., and a "dirty" place with soldering iron, vise, drill (ideally drill press), Dremel, pliers, nibblers, files, saws, etc. Do your construction in the dirty area, and your measuring/testing/breadboarding in the clean area. My clean area is the computer desk, and I've got a stand-up counter (old kitchen counter, relocated into the garage) for my dirty area.
Except I just realized, I do my soldering in my clean area, only my construction involving drilling, cutting, grinding, and filing goes to my dirty area.
As for ESD, it's not usually a huge concern for hobbyists, but if you can cover your work space with an ESD mat, that's a good thing to do. The risk depends somewhat on your climate (humid is good), type of work, whether you have carpeting, etc.
If you can avoid carpeting, I would do so, for two reasons. One is the ESD issue, and the other is the issue of lost screws and other tiny parts. You WILL drop tiny things, but it's easier to find them on a smooth hardwood floor, particularly if you can keep it uncluttered and frequently swept/vacuumed. But things do bounce and travel more on a smooth floor.
The desk space issue is a good argument for a modern DSO, like the ubiquitous Rigol DS1052E. They take up a tiny fraction of the desk space compared to an old analog scope, and are really easy to move around. It's also an argument for handheld meters over bench meters.