Tyres
Don't fit oversize rubber on your bike just because modern bikes have big tyres. They were designed for it. The RD wasn't.
Best sizes to go for are 90/90 on the front and 110/80 on the back. These are the closest low profile match to imperial sizes, and usually the manufacturers recommended sizes. And they handle well too. I have been told a 120 won't fit in the swinging arm, and so not tried it. It wouldn't handle even if it did fit. When you squeeze too large a tyre on to a narrow rim, the profile gets distorted. As the side walls are squashed into the rim the tread forms a more circular profile, resulting in less contact patch and the risk of the tyre popping of the rim. Try it if you must but don't say I didn't warn you. Watch out for Insurance legality. If a manufacturer doesn't recommend a tyre, your insurance might be invalidated, even if they fit and work well. At least, they might wiggle out of a claim on the grounds that your tyres weren't 'fit for purpose' or some such crap.
H or V rated ?
The choice is yours. H rated is enough, though Vs might be more stable/grippy.
Brand
At the moment, the best I've tried and would thoroughly recommend, along with loads of other RD riders, are the Bridgestone BT35 and BT45s. I am running them at the moment and they are by far and away the best tyres I have fitted. Metzeler ME33/ME99 are a good combination to go for. Also the Michelin M38/M39 or M48/M49 combinations work well (did 1000 miles round France on them, two up with camping gear, no problems!). Avoid Pirelli Mandrakes at all costs. They're crap. Also Pirelli Phantoms ain't too hot either, OK dry but in the wet... Avon Road Runners ? No thanks. These are my personal preferences and views I have learned from experience. Yours may differ. Some might say "I've used brand X for 20 years and I always scrape the pegs etc etc" but times and technology change. Wake up and smell the rubber! It's MUCH better these days. I would recommend you try some newer tyres. You WILL be amazed. Ultimately though, it's your choice.