The A300 was the middle of the entry level Sony's a couple of years back.
It is the same as the A200 (which I have, now as a backup to my A700) but with the addition of live-view and a slightly reduced viewfinder (a consequence of the way Sony implemented live-view).
At the time they A200 / A300 / A350 were very good value as entry level DSLR - though now they are a couple of years behind current models, which is apparent if you need to go above ISO 800 when the images can be quite 'noisy'.
There main downside is that you are (potentially) committing yourself to the Sony (Minolta) Alpha mount for lenses. While there is a reasonable range available, including the older Minolta AF lenses, there are a few gaps compared to Canon / Nikon - but these tend to be at the higher priced end of the market (so not that much of an issue for the average amateur). It may also be harder to get the lenses you want locally.
On the other hand, if you have been offered a good price, and are just wanting to try DSLR photography then the A300 should cover most bases in terms of what you can do, with the added benefit of in-body stabilisation helping take shots at lower shutter speeds without camera shake impacting the image quality.