First of all, welcome and I hope you enjoy your coming Alfa experience. Personally, I've just turned 27 and bought my first Alfa at 18/19 and not looked back since and am now on my 6th! There is plenty of experience on these pages so do soak it all up.
I would hasten to add that the technical section may look a little off putting - but remember that section is for people seeking tech advice so whilst it may look off putting people don't post to say how amazing their car is - they're probably out driving it instead. So don't get put off my the fact there seems to be a lot of people looking for tech advice, that's what we're here for.
The 2.4 is great motor. It traces its routes back to early 156 models where it started out as 10v 136bhp motor. The addition of digital boost controllers saw it increased to 140bhp and then 150bhp in 10v form and late in 156 production 175bhp with 20v. The motor was significantly upgraded for the 159/Brera/Spider and started out life in these cars as 200bhp before reaching its final fighting weight of 210bhp a short time later. The 210 motor is best of the bunch.
That said, don't expect it to be amazing on fuel and don't believe the book figures for MPG, check out something like fuely to see what people are really getting. Town driving especially these are bigger heavier cars that are not great on fuel.
As stated above, the known issue with gearboxes relates to the M32 gearbox. If you're a Vauxhall guy you will be familiar with this from a lot of their range, corsas, vectras, zafiras to name a few share the box. However, Alfa only fitted this box to the 1.9jtd and JTS 4 cylinder models. The gearbox fitted to the 2.4 is the F40 and is the transmission equivalent to a brick out house.
Early models had an issue with the incorrect steering fluid being used at the factory... d'oh! The car should have green fluid in it but Alfa used red. The red stuff can cause issues with the rack, but then so can changing from red to green, so look for a car with green fluid. The power steering reservoir was also revised mid-production as there were issues with PS fluid foaming up, so if there are signs of this in the PS fluid tank, leave. For what it's worth my car is a 58 reg and has the old style fluid tank and I don't have an issue.
The only major thing to look out for realistically is tin worm (rust) as people have mentioned. It is becoming apparent that some sub frames are starting to suffer and rust through. If you don't mind a bit of painting treat with rust proofing when you can to help her along.
Other than that it is only minor niggles like inner edge tyre wear, as the factory settings have the fronts toed in slightly. this was revised to 0 toe later but if it is out the tyres will wear.
Being larger heavier cars this does take their toll on suspension bushes, so listen out for knocks and squeaks. Damp weather and squeaking / rattling tends to mean that the top arms are failing, approximately £60 each for these. The bottom arms are more expensive at around £160 each but there are pattern parts starting to emerge for around £100.
Something that bothered me when looking - the centre console. Look out for people that have had a bunch of keys on their car key, as this scratches and dings the console and annoyed me.
Worth noting that around mid 2008 the model underwent a 'facelift' revision. Nothing externally changed but internally the seats are a different design and there were a few minor tweaks and improvements here and there. The easiest way to tell if you are looking at one of these later 'revised' models - check the aircon control panel and see if there is an "Off" button for the fans. On earlier models this was a "Mono" button.
Last thing to add - cambelt. Service manual if you read recommends changing the belt every 5 years or 4 for colder climates, so the belt should have been done and if not will need to be done. Historically Alfa's are not something you can push your cambelt luck with.
Good luck with your search - drive a few, see if they suit you and make your decision. They're a bigger squishier cruiser than the 156 and if you want a real drivers toy I would recommend the 6 over the 9 but the 9 is a great car none the less.