Can I use a non-AF lens with a Canon 1000D AF body. Canon lenses use in-lens motors for focus, and the only connection is electrical, so I don't see why not. What type of mount and lens should I look for? I like the convenience of AF, but there are times when I don't need it, and non-AF lens are cheaper.
AF = Auto Focus; MF = Manual Focus
If by non-AF lens, you meant a manual-focus lens, the answer is yes. You can use manual-focus lenses with your camera. Depending on the particular lens you are interested in, you may need an adapter.
EF = "Electro-Focus". This is the name of the Canon mount.
If you meant to type non-EF lens, the answer is also yes. You can use adapters to attach non-EF manual-focus lenses to your camera. For instance, adapters are available for M42 lenses. However, there are limits on which lenses you can use. See Can I use lens brand X on interchangeable lens camera brand Y?
To get an idea of what lenses and adapters are available, you can search for "EF lens" and "EF adapter" on various shopping sites. However, be aware that "Using an adapter most of the time is masochism.", as Agent_L has commented.
Unless you are after a specific effect, such as fish-eye or particular bokeh, you would be better served by getting a modern general-purpose lens, such as the EF-S 18-135mm/F3.5-5.6 IS USM, which is fairly inexpensive. Despite being a zoom lens, it will deliver much better image quality than most adapted manual-focus lenses.
As noted by Frank, your camera has a crop-frame sensor and EF-S mount. Lenses with EF mounts, made for use with full-frame sensors, will work with your camera. EF-S lenses made by Canon can be identified by an extra ring of plastic that prevents them from being mounted on full-frame bodies. However, EF-S lenses made by third parties may still mount on full-frame bodies. In this case, they may be identified by heavy vignetting in the images taken with them. Care should be taken to ensure that lens elements do not obstruct and damage the mirror.