I am looking for the "base speed" if you will for AD&D 1st edition PC races and can't find it anywhere. So I am wondering how fast are the PC races in 1st edition AD&D?
Under one reading, PC movement rates are a function of only Encumbrance (p. 101–102), and normal un-encumbered movement rate is 12". However, this comes with a very large caveat:
The text of the Players Handbook and Dungeon Master's Guide both omit any mention of movement rates varying with race. However, the Monster Manual gives dwarves (p. 35) a move of 6" (which is further confused by including the reduction from encumbrance of "typical" gear), and gives halflings (p. 50) a movement rate of 9". As a result, the actual rules as written are ambiguous and it can be argued either way.
Different groups and DMs have decided different ways on this point. Which way you choose to go is entirely up to you. A consistent 12" base movement rate does simplify movement and travel with a mixed group, while varying movement rates can feel more "realistic".
It's worth noting that other editions (both earlier and later) have explicit base movement rate differences among the races (notably, dwarves are sometimes and halflings always are listed as having the equivalent of 9" movement rate). It can easily be argued that the lack of movement-by-race is an oversight in the PHB and DMG, and that every other TSR edition giving varying movement rates provides a simple answer to how it "should" be in AD&D. Still, it is up to you. Whatever is convenient and most pleasing for your group: do that.
Personally, I have always gone with base movement rates varying by race, with dwarves and halflings getting a 9" base, but then my early DMing was heavily influenced by our mix of 1st and 2nd editions, and 2nd edition does make this explicit. From experience, the disadvantage of varying base rate is that a mixed party constantly has to slow down for the shorter members, especially when dwarves are frequently slowed even more by the weight of armour and gear. This often became a frustrating detail, and I can easily see the wisdom in doing away with it and setting base rate to 12" for everyone. Groups that are more into the resource-management part of the game might consider that "playing on easy" though, and prefer the extra detail from varying base rates.