Are you talking about the preset monk class or just a monk sort of character?
If the preset class.....
As a general rule, I shy away from signs that give bonuses to attributes for which the race already gets a bonus. Bosmer already get a bonus for speed and agility, so The Thief will just add to that. Though it will also add to luck, which is always a good thing, particularly in the early game. But the character will already have plenty of agility and speed, so more isn't going to be of that much benefit generally. There is one quirk with the preset class though-- it uses all three agility skills and two of the three speed skills as majors, which means that the character will never be able to get really good bonuses for those attributes, so a bit of an additional head start on them could be of benefit. And this is particularly true if you're going to be focusing more on marksman than on hand-to-hand, which will make agility that much more important.
At first glance, I'd tend to lean toward The Warrior (at least as far as attribute bonus signs go). Bosmer take a penalty on strength and have normal endurance, but hand-to-handers really need strength and endurance, arguably even more than other melee fighters, since they can't upgrade their "weapon" and hand-to-hand fights are up close and take a long time, so they will get hit quite often and need all the hit points they can get. As noted, this is less important if you're going to be focusing more on marksman than on hand-to-hand, but even with that, I'd still consider The Warrior, just to make up for the Bosmer strength penalty and to add to endurance, which is easily the most important early game attribute.
The Steed could also be useful. The only bonus you get for that is for speed, but it's a huge bonus, and with the Bosmer bonus to speed, it'll give you a starting speed of 70, which is incredibly fast for the early game. The only real use for that though is moving in and out of melee range and jumping relatively long distances (and, of course, simply traveling faster). It's of limited use, but it could be at least interesting.
Now, all that said, there's an argument against using any sort of attribute-boosting sign. The bonuses you get for those signs are really nothing more than a sort of head start, since all normal attributes max out at 100. Given time, any character can build up any attribute to any amount (up to 100), so later in the game, those bonuses that you got won't make any difference at all. 100 strength is 100 strength, and it doesn't matter which race has it or where it started from. It's all the same at that point. So, in that sense, birthsigns that give magicka bonuses or powers are more useful, since they'll remain throughout the game.
If you're planning on using any magic at all, a magicka boosting sign is definitely the way to go. Magicka bonuses are the only ones of the birthsign bonuses that are permanent-- no matter how much magicka your character has naturally, the bonus for the birthsign will be added on the top, with no maximum. Mage is the easiest-- an extra 50 points of magicka with no side effects. Atronach is the biggest bonus, but stunted magicka is a hassle unless you know how to work around it (and, IMO, is still a hassle then). Apprentice is only good for roleplaying-- the 100% weakness to magic is a HUGE liability, so it's only worth it if you're interested in playing a deliberately gimped character.
Beyond that-- I'm a big fan of The Lord with a hand-to-hander. The Blood of the North lesser power is the most massively useful healing spell in the entire game, by far. It delivers a whopping 90 points of healing for a cast cost that's a tiny fraction of what it would be for the same effect as an actual spell. Since it's a lesser power, you can cast it as many times as your magicka affords, and since you'll almost certainly start the game with fewer than 90 hit points, it makes you just about indestructible for at least the first few levels. And if you invest a few bonuses in intelligence early on, you can easily get to the point at which you can cast it back to back, which will keep you virtually indestructible for much of the game. That's particularly useful for a hand-to-hander, since you have to get up close and fights tend to take a long time, so you'll take a fair amount of damage. Cast BotN at the beginning of a fight and you can actually see your health go down, then back up, then back down, then back up....
And that should be plenty for now.....