You are about to do what we did back in 2009 - buy a 147 as our first Alfa.
There's a lot I could tell you - some which might put you off, but on the whole you need to approach buying an Alfa in the same way as any other second hand car.
Check for service history, or evidence that the car has been well looked after. It is probably fair to say that most Alfas are owned by enthusiasts but that doesn't meant they know how to look after them. I'm no expert but have learned a lot over the years and have had my share of big bills - especially in the beginning.
Apart from the obvious such as driving it before you buy it and checking that everything works (many Alfas are well specced up so check all electrics and gadgets to check that they work), make sure it's had the cam belt and timing variator changed - or if not factor that in to the buying price. Just had mine done for £430 inc. VAT.
Cam belts are supposed to be done every 3 years or 36000 miles now (used to be 5 years and 72000). My Alfa man says its ok to go 5 years still - it's the mileage that matters.
When I get more time I'll see if I can list a few other things to consider for you too.
No doubt you'll get some great pointers and suggestions form other people on here too.
Good luck and enjoy the journey. Alfa's are special and not run of the mill cars.