Welcome
A Minor is absolutely fine as a run-around, and much more! I do 10,000 miles a year in mine and have no reliability problems at all. You do need to keep on top of simple maintenance tasks such as setting the points gap, greasing the suspension, etc, but they're very easy and people on here will always be willing to help. If you get a Minor, you really do need to be willing to learn how to do bits and bobs on it yourself, as otherwise you could very easily end up spending huge sums at garages.
For daily use, a 1098 car would probably be best. Besides the extra power, the gearing is higher (giving more relaxed cruising), plus the brakes are better. However many earlier cars have been upgraded to 1098 spec, so don't discount an older car.
Disc brakes aren't really necessary on a standard car, with the possible exception of if you live in an extremely hilly area. The original drums are fine as long as they're well maintained, although if you're coming from a modern car the feel of them may take a little getting used to.
Seat belts are easily fitted, although on 2dr cars the shoulder mounting point (in the front) is less than ideal. I found inertia belts to be very uncomfortable when mounted there, so you might better off with a static belt. All post-'65 cars will have front belts fitted, as they have to by law. Rear belts can be done, although if inertia ones aren't to look horrible (mounted in the middle), they do require a bit of effort and ingenuity.
Owners do tend to wave, flash lights, etc.
[img]http://i31.photobucket.com/albums/c390/chrisd87/DSC00749.jpg[/img][img]http://i31.photobucket.com/albums/c390/chrisd87/med_gallery_128_45_1416415.jpg[/img]
Sarah - 1970 Minor 1000 2-dr
Maggie - 1969 Minor 1000 4-dr
) , before my current car needs re-moting / taxing and insuring, getting my own.
) so I can hopefully get the bi-monthly!