I quite like Schwalbe Blizzards, they're about £11-£13 each from somewhere like on-one. They're not puncture proof, but there does seem to be enough material to stop all but really stubbourn thorns/glass.
This time of year I'd be getting soemthing heavier and as higher volume as will fit for comfort and puncture resistance as the road surfaces are horrible. Even really racey bikes will take 25mm tyres (which doesn't sound like much, but it's almost 20% more volume than the standard 23mm).
And get some mudguards, SKS raceblades fit most bikes, or chromoplastics if they'll fit and it has eyelets. You'll be supprised how often you want to ride, but it's just rained so if you go out the roads are wet and therefore so are your shoes and arse, mudguards mean you can go out in anything except actual rain and be dry.