If your budget is £16k then you'll be right at the bottom end of the i6 range.
Not a good place to be.
If you wish to look for a GTA as per your username then you'll need to double your budget at least. If you want a GT then double it and add some.
A decent standard Vantage can be found for approx £20k to £25K.
Service history isn't everything on a car as old as these will be, but it's often a requirement to see where it HAS been serviced or if done by the owners, ask to see the invoices for genuine parts.
The i6 will cost less to run and maintain, but is an older car. The Vantage is better but running costs and maintenance costs will be higher.
The GTA and GT are a marked improvement, though the GTA lacks the x-factor due to the auto box holding it back on several counts.
Of course I am a little biased to the GT as I own one, but then I only bought a GT as it was the best of the DB7 range with only the Zagato and AR-1 competing, but either over priced or non-practical.
So basically you need MINIMUM, £20k GBP or you'll end up paying more over time with lot's of repairs and niggles. For a decent DB7 you should be up around £25K GBP, as you move higher the car quality will increase but at a premium.