Don't bother with a diesel if you're only doing 3k miles annually. They only make sense when doing 10k miles or more.
You can definitely get some good cars for around that money in the UK. The MAJOR thing to watch out for is the cambelt service. It needs changing every 3 years or 36k miles (iirc), whichever comes first, and is a relatively costly service so definitely make sure to check when the belt AND tensioners/water pump were last changed. If it is due for another cambelt within the first 6-12 months of your ownership it will give you some bargaining power.
Other than that, knocks or thuds when going over bumps at low speed is usually a sign that the front wishbones and bushes need replacing. It can also suggest that the ARB bushings need replacing as well. This isn't overly difficult or major and can be done yourself if you've got a spare weekend and the right tools. Though the parts bill will definitely be a few hundred quid (and only ever buy TRW wishbones).
If on a test drive, the car doesn't get to 90 degrees on the temp gauge and pretty much sit there, that indicates that the thermostat needs replacing. Incredibly easy job and about 40-50 quid in parts and a definite DIY (2-3 hours at most - less if you're handy with the tools).
If the clutch makes a slightly groaning or scraping sound when engaging/releasing the pedal and feels quite heavy.....walk away. Signs of the clutch release bearing going and will mean a new clutch assembly in the not too distant future.
I'm sure others will add many more things but they are some of the basics to look at. Also check Alfa Workshops buyers guides for 147's