For mapping footways (ways that are unsuitable or forbidden for vehicles) you can either choose between [highway=footway][1] or [highway=path][2]. Both tags *can* express the same when combined with certain [access][3] tags. See the [default access values][4] for details.
(Theoretically you could also use a completely different highway category and apply lots of access tags but you shouldn't do this as this is nonsense and most renderers and routing applications also use the highway class for additional implications).
If the ways you want to map are mainly for pedestrians and forbid bicycle usage, then go for *footway*. If they allow bicycles then you can either add the [bicycle][5] access tag when using *footway* or use *path* without any additional tagging.
If you are curious why there are two different tagging methods then I suggest reading these answer to related questions: [one][6] [two][7].
Regarding *tracks* and *services*: A [track][8] is mainly for agricultural and forestry vehicles and thus often found outside of cities or at the border of them, but rarely inside. A [driveway][9] instead is a way for vehicles leading to a property. Both are unsuited for tagging pedestrian-only ways. Take a look at [this question][10] for more details on them.
[1]: http://wiki.openstreetmap.org/wiki/Tag:highway%3Dfootway
[2]: http://wiki.openstreetmap.org/wiki/Tag:highway%3Dpath
[3]: http://wiki.openstreetmap.org/wiki/Key:access
[4]: http://wiki.openstreetmap.org/wiki/OSM_tags_for_routing/Access-Restrictions#Default
[5]: http://wiki.openstreetmap.org/wiki/Key:access
[6]: http://help.openstreetmap.org/questions/7015/tagging-public-footpaths-for-routing/7064
[7]: http://help.openstreetmap.org/questions/7538/path-versus-footwayhttp://help.openstreetmap.org/questions/7538/path-versus-footway
[8]: http://wiki.openstreetmap.org/wiki/Tag:highway%3Dtrack
[9]: http://wiki.openstreetmap.org/wiki/Tag:service%3Ddriveway
[10]: https://help.openstreetmap.org/questions/18103/choosing-highwaytrack-vs-driveways-and-paths
