Riding alone is great as long as you are a little bit self-sufficient and can take care of small repairs. A repair kit with a few patches, cement, and a pump or CO2 cartridges is a really good idea. That way you can repair your flats anywhere, and do not have to waste too much time or walk. You can find those kits in any bike shop and they are very small so they won't take up too much space in your pockets.
As per tires, some of my riding buddies use gatorskins and love them. I don't like them much, heavy rubber and low psi, not my favorite...
I tend to ride Tufo tubulars or tubular clinchers more than anything else - so all I bring on my ride is sealant and a couple of CO2 cartridges. When I ride clinchers then I put one or two patches and some glue in my pocket with the CO2, just in case.
If you think you can end up quite far - too far to walk if you have a mechanical worse than a flat - I would highly recommend that you learn how to make a few basic repairs, and carry along a small multitool and a masterlink or a couple of chain pins. I've seen a few people with broken chains on the road, up for a long walk - and it doesn't seem to be a lot of fun.