Thanks for the added info. There are 3 things to consider here then.
The first is picture quality i.e. camera output. This is largely governed by the choice of camera body and lens, both of which contribute to the quality of the output. Most, if not all, DSLR camera bodies will be capable of giving you A4 output. They are mostly 6MP + resolution which is more than sufficient. The quality of output from the camera, as you'd expect, can improve with price but still depends on a competent user (see 3 point below). The more expensive the camera, the more skill required to use it is a good rule of thumb, although not absolute. The choice of lens is very important too, and price is not always the deciding factor. For example an 85mm prime lens (i.e. no zoom) at £300 may be better for portrait than a £600 18-200mm zoom lens. However, you limit yourself on what you can do with a fixed 85mm lens versus and 18-200mm.
The second factor is lighting. If you want studio quality shots then you need studio lighting. These are the large lamps with umbrellas or shades and a vinyl backdrop. These start at c. £200, require a lot of space to use properly (probably 10 foot square of clear space), and require a degree of practice and expertise to use.
The third factor is the ability of the person using all of the above kit. You can have the best and most expensive kit and still be the worst photographer in the world if you don't know how to use it. you could be a natural from the start, or it could take months or years of practice to get it right.
I would recommend finding a good independent camera shop and talking them through what you are looking to do, and let them show you what's available.