For your purposes a 2-point sling is probably best. A 2-point sling is a very common design and probably what you are already used to.
A one-point sling is attached to the rifle at a single pint, usually at the rear of the receiver. They are favored by people who do a lot of work from vehicles or other situations where maneuverability is a major requirement. A one-point will allow the rifle to flop around a lot while you are walking thus making it less comfortable in the long run. Also, one-points don't aid much with stabilizing the rifle, if you use your sling for stability when shooting.
A 3-point would also work, but probably isn't necessary for what you are planning. 3-points are usually set up similarly to 2-points, but they give the shooter a few more options for how to use the sling. Personally I don't think they are worth it. I used one for several years and spent the whole time wishing I would one day be allowed to replace it with a 2-point. Other people think they are great.
Also, I would suggest a padded sling if you are going to be walking around a lot, and wider slings are generally more comfortable than narrower ones.
I like my Vtac padded 2-point a lot. There are many other good options out there.