The old A3 1.8T is disappointing car to drive IMO. Fairly quick, but its a scrabble wagon and feels wooden. However, it looks good for its age/price but there don't seem to be that many around in good condition. Think you'll also struggle to find a 5 door, average mile car for £3k since the 5dr came out towards the end of the lifecycle for that particularly car.
As for the 3 series, a £3k E46, a 1.9 is going to be a waste of time. It's also going to be OLD and slow, and also likely to need some money spent on it. You could pick a 6cyl E46 for that sort of money but it won't be average miles, unless you're referring to average miles being 12k x each year since registration, in which case you'll be looking at a 100k plus car....
You'll definitely stuggle to find a B6 1.8T for £3k.
For this sort of money, you need to be looking at Mondeos and Mazda 6s. For £3k you will a lot of car for your money - the Mazda6 in particular is v.good value at this price point. For example:-
2003 03 Reg MAZDA Mazda6 2.0 TS2
Price:
£2,990
* 90,619 miles
* Manual
* BLUE
* Petrol
* Hatchback
* 1999 CC
5 Doors, Manual, Hatchback, Petrol, 90,619 miles, Metallic BLUE. ABS, Adjustable seats, Adjustable steering column/wheel, Alloy wheels, Climate Control, Computer, Cruise control, Driver airbag, Electric mirrors, Electric windows, Front armrest, Lumbar support, Immobiliser, Passenger airbag, Power assisted steering, Rear armrest, Remote locking, Side airbags, Radio/CD Multichanger, Rear headrests, Traction control, 9 months MOT, Direct from company, superb condition, Totally original, Anti theft system, CD, Heated seats, Leather seats, Leather upholstery, Metallic paintwork, Full Service History. Insurance Group:9, £2,990 p/x welcome
'Direct' company car, full history, leather, bodywork looks umblemished, paintwork still glossy etc. With a bit of haggling you could knock off £200-£300 off the asking price. That's a heck of a lot car for £2800 and you'll also get that famed Mazda reliability which is going to be useful for a high mileage car.
http://pictures.autotrader.co.uk/ATD_web/servlet/media?id=808444760
http://pictures.autotrader.co.uk/ATD_web/servlet/media?id=808444863
http://pictures.autotrader.co.uk/ATD_web/servlet/media?id=808444813