If you're looking at creating a new character for the purpose of Mining and Herbalism (especially since you can track all types of nodes now), here's the absolute best class benefiting from both speed and utility:

Tauren Frost Deathknight (with Unholy Presence)

What's also nice about DKs is that you start at 55 and you can practically level yourself to 80 from just gathering. By the time you hit 80, you'll have enough to purchase all flying upgrades including [Master Flying] (4000G with Exalted Rep) to get your 310% mounted flying speed.

Benefits:

+20% Mounted Speed
+15% Foot Speed (Stay in Unholy Presence)
Cultivation allows you to herb very quickly
Path of Frost
100% Underwater Movement (*with [Hook of the Master Angler])

Frost abilities are also awesome for crowd control and survivability:
- Hungering Cold!
- Freeze, silence, or slow down players and NPCs alike.
- Frost Fever disease on enemies causes a 50% reduction in speed for 10 seconds. Howling Blast hits multiple enemies too.
- Immunity to knock-back or pull mechanics (other DKs).
- Fast escape skills (if you just want to keep gathering and avoid combat).
- Summon ghouls to keep NPCs busy while gathering.


* All of the benefits listed above make this class ideal for Fishing (Path of Frost FTW) as well, and the class is perfect for beating the Stranglethorn Fishing competition. Just make sure you do your research before competing!

Other Notes:

Mining and Herbalism used to benefit from Haste Rating, but I'm not sure if this is still the case. Herbalism might, but I couldn't tell with Mining - if you know for sure, please let me know.

With Haste Gear and Lifeblood (Herbalism ability), you could pop it every 3 minutes for super-speed mining if you're in a rush. =]

If you're interested in Herbalism only, I would recommend the Tauren Druid race/class instead. You don't get the extra +20% mount speed, but when you're in Flight Form, you don't have to "dismount" to farm herbs which is very nice (for avoiding combat as well). Skinning also goes well with this build, since you can remain in Flight Form the entire time (easy to skin/herb then escape.)

Unfortunately, if you want mining and herbalism - you have to sacrifice the mount/dismount time. It's worth it though for all of those precious herb and mining nodes out there. =]

On a side note, with Death Gate and your hearth set to Orgrimmar, it gives you very easy access to UC, ORG, Blasted Lands (then Shattrath), and the portals to Cataclysm locales. During downtime, I would also recommend doing the Argent Tournament daily quests to get the [Argent Pony] for remote access to your banks.