Tyre size

Used Vittoria Zaffiro pro 28mm over the last winter. No issues and dead cheap at wiggle.
It'll also depend what your local roads are like.

If your rims will accept tubeless look at the new "Schwalbe G One Speed" (maybe a bit late for this winter) 30mm all rounder.  Having used tubeless now for a year, I have had no punctures on three bikes, one is a mtb for off road.  Just a thought

I use Conti 4 Seasons religiously in winter because they're designed to stay grippy in cold condition, which they do. I wouldn't get hung up over their puncture resistance though, I've had plenty.

No doubt I'll get a flat tomorrow morning but I've gone puncture free for a year and a half while riding through the middle of London most days. I've clocked more than 3500 km and all thanks to the much despised Continental Ultra Sports II 700 x 28s that came stock with my bike. I only ever read poor reviews of these tyres, most claiming sub 100 km durability and appalling puncture protection from kilometre zero. I was convinced my old hybrids Marathon Plus boots were the reason for my previous years of flat free commuting and with my hopes low, waited for my inevitable date with a rainy night roadside repair. Yet with every day and kilometre that passes underneath these Ultra Sports, I am beginning to realise that you don't need the highest available level of protection at all. It's simply not necessary. Which is great news when you consider the numerous benefits of a lighter weight tyre.

28mm will cut down on weight but will be less comfortable over rough surfaces. However, if you're only doing 5 miles a day, the physical difference will be negligible and the psychological difference beatable.

However 2. Unless your ride involves turning hard at speed 32mm rubber won't likely be the cause of any serious injury.

You might do worse than try Marathon Greenguards.  They are a little lighter, a little more comfortable and quite a bit cheaper than the standard Marathon.  I've had 'em and have no hesitation recommending them highly.

The tyre website bicyclerollingresistance.com reckons they are top choice for your sort of riding.

Marathon Supremes are a bit more expensive than the Marathon Plus, but much much lighter.  32 and 35 available.

In the Conti world the 4 Season goes up to 28, and you can get Gatorskins in 32. I run those for commuting on my CX bike - excellent puncture resistance and the extra volume will help deaden the impact of the road surface. Not particularly exciting to ride but look good. 4Seasons are a bit faster but not sure its worth paying the premium, and they're not available in a 32.

That rim is a shade under 21mm wide externally, so mid range in width for road specific wheels.

Shimano state 28mm tyre max, but you should be able to run 32mm without issue. Don't go as far as 35mm though as you'll end up with a giant squishy lightbulb shaped tyre and quite probably some serious handling problems - particularly in turns.
As for tyre choice, the marathon plus is a great tyre for puncture resistance and longevity but it's about as dull as you get in terms of road feel and handling. It also weighs a ton.

I've used marathon supremes in 32mm for commuting and they're excellent. If you look at the German websites you can get them for much less than anywhere in the UK.

Coincidentally, I built up a flat bar Kaffenback this weekend and went shopping in town today. I'd fitted a used pair of supremes and at about 75psi they were both fast and comfy.

The Schwalbe Durano is also available in 32mm and has both good puncture resistance and handling. I've used the 25 and 28mm versions as winter "training" tyres for years.

If you're looking for high levels of puncture resistance there's also the Panasonic Ribmo. However, the Ribmo is as dull and lifeless as the Marathon plus.

If you tell us what style of riding you plan to do, I'm sure the group can generate loads of options!