Welcome aboard mate.
Firstly, has it had its cambelt, tensioner, waterpump and variator change? If not, then you are going to be looking at around £500 minimum including the service.
The cambelts need changing every 36,000 miles / 3 years on the Twinspark Alfa engines, so if this has not yet been done then it's well overdue. It's a major job and it's quite necessary to get the waterpump and variator done at the same time.
To be honest, if they've not listed it in the advertisement then I really doubt it has been done.
From your description it sounds quite decent, but do bare in mind it's on a 51 plate so will therefore fall into the new tax groups, so find out which one it's in first, as you might be better off buying an older example. (2000 and before)
From what I've heard on the forum, the 1.6 156 is a decent enough little motor, but personally I'd want at least a 1.8 engine in a car that big. I've had both a 156 2.0 TS, and a 156 2.5 V6, both quite cracking performance wise, but the V6 was a heavy drinker,
The 2 litre Twinny though was quite decent on fuel and went like the dickens with better handling than the V6, it's the one I'd go for personally. I think you'd suffer from the decrease in power to be honest otherwise.
Does the car come with FSH, dealer books, all keys etc etc? £1200 'sounds' like a good price, but that may be because it needs a full service and all of the cambelt work etc doing. Ask them if it's been done and at what mileage, if they say it hasn't been done, then that's not an issue, but you will need to get it serviced and have the cambelt changed the instant you get it as it's already running on borrowed time. £1200 + £500 (Minimum) is £1700.
£1700 could get you a cracking 1999 156 2.0 TS SP3 with about 70K on the clock, belts changed etc etc, FSH.
Have a think about it mate and let us know what you decide!