Welcome to AO
Both myself and one of my sisters have a 1.8 16v 155 (effectively the saloon version of what you have). I'm also a mechanic- well, a partner in a profitable garage business and an Alfa owner of 15 years experience. I think I can shed a little light on things.
The mileage of the car isn't really a worry (sister's car is still really strong, usually driven awfully fast, and it's on 149k). You'll find clues as to whether it's a good 'um or not- (electrics, gear lever slop and door and handle operation etc).
Hopefully the wipers are smooth in operation- wiper motors are poor.
No suspension clonks- rear suspension trailing arm bearings, front wishbones and front struts are all parts which can wear. None of these is too expensive to do, but a number of like faults can make a car not viable. Check front tyre wear regularly. Incorrect alignment or suspension wear can produce pronounced inner shoulder tyre wear which will usually severely reduce tyre life.
Gearboxes can be a bit weak, watch out for noisy gear engagemant or jumping out of gear. Your car may/may not have already had a clutch. Hopefully by now it's also had a clutch slave cylinder (not expensive).
I'd agree with Michael. However, I wouldn't worry too much about oil and filter history. Sure, you really must keep the oil level topped up regulary and don't let it fall very much. However, previous owner negligence in this department will not necessarily condemn the engine. Also, use any good brand oil/filter combination. Chances are, the oil filter is made by the SOGEFI group which supplies Fiat Auto anyway.
The cam belt and pulleys should be changed every 40k (to be safe). A visual check may give clues as to age and mileage, but if there is doubt, budget to have this changed soon. Last one I did was £260 inc vat. Add about £100 for a variator (retail prices). A worn inlet cam variator will make the engine sound like a diesel, but it will not damage the engine- it just becomes noisy. As the inlet cam needs to come out, this would be changed only whilst changing the timing belt etc.
Other service stuff can be expensive. Spark plugs should be platinum tipped and good for 60k. NGK part numbers are BKR6EKPA and PMR7A. BTW, there are 4 of each and they cost about £6.50 each+vat (trade). Non platinum alternatives are available, but they do not perform quite so well, nor last as long.
The good news is that the fuel and air filters need only be changed every 2nd or 3rd service. The service interval is 12.5k, but I prefer to only go 10k between services. These are high tune engines, and the 1747cc engine thumps out 140bhp.
Generally, the are very well built (for Mediterranean cars) and often outlast much more mundane counterparts. However, it really does pay to keep on top of them. I've seen plenty of neglected examples which would take many hundreds of pounds to bring pack to a good level of maintenence. That said, £1000 can buy a really clean car with virtually no faults, and I really mean no faults. Not even needing a timing belt within say 10k.
If anything quite expensive is needing done soon, sometimes ebay can provide significant savings for parts. However, with things like lambda (exhaust oxygen) sensors, I find it best to fit an OE quality part.
Specialist suppliers like Alfashop.co.uk can supply the right parts at affordable prices.
Hope you've got a good 'un and enjoy Alfa ownership.