Onto the Sleeves
In Border select mode, click on the edge opening for the arm, and then switch to the front view and hold down SHIFT and pull outwards to start the sleeve.
I moved the edges down a bit and rotated them to an angle. Then I selected just the top sleeve edges and connected just them. In vert select mode, I selected the new edge vert and connected it to existing verts (make sure to switch to perspective and check the back to make sure to connect it properly there).
Then in Vertex select mode I moved the vertices around so that they fit the shape of the arm better. Once I had the shoulder started, I selected the border of the sleeve and while holding down SHIFT I pulled it further down.
Continue working your way down, and use scale on the selected edges when you need to make them smaller because this will make them smaller from other angles as well and reduce the amount of fixing you'll need to do from the top/side views. It's hard to get a good second angle on the arm so you'll have to do a lot of tweaking in perspective.
Another important thing to take into account is how the arm will deform when rigged and animated. With this baggy simple sleeve, a lot of geometry really isn't needed, but if you have too little geometry in the joints, they will deform poorly. I decided that I needed one more loop at the elbow, so i selected the edges just below the elbow and clicked connect and adjusted the Slide so that the new edge was created near the elbow.
Time for some optimizing
When you're tight for polys, any extra or not-totally-necessary edges are important to remove. The arm has a lot of edges going around it - more then it needs, so I went back in and started welding together any areas that could afford it.
Do a general all-over pass for anything you can optimize or tweak at this point, and set the smoothing groups on the sleeve.
Okay, I know this is a big jump... and I'm sorry, but I honestly didn't feel like including a 'how to make a head' tutorial in with all the rest of the stuff I'm covering here. There are a gazillion 'face modeling tutorials' out there already... in fact, I, even wrote one already. So use one of them...
A few things to point out - There are no holes in this head for the mouth or eyes. It depends a lot on the game, and what the goals are, but a lot of very low-poly characters for games just have the eyes textured straight on the geometry with the rest of the face. Not actual geometry eyes. Having them painted directly in the texture tends to look better with really low-poly characters anyways, plus it uses a LOT less geometry.
If this character was going to need to talk during cut-scenes, I'd set it up with a mouth that could open and some very simple geometry for the interior of the mouth, but I'm not going to bother with that here.
One other thing to point out is that I selected the collar of the jacket and pulled in some faces so that it's not just a floating flat poly edge anymore.
So on to the hands
Most all of the hands detail is going to be in the texture. I'm going to leave the ring and pinky fingers connected to save polys, and have the hand in a loose slightly-curled position. This is using the assumption that the hand will not be animated. In this position the character can look like it's hand is just relaxed, but it can also look like the character is holding something.
Off to the side of the character, go to the top viewport and make a box. The box should be short in depth, and nearly square from the top view.
Select the two edges of one of the sides and connect with TWO SEGMENTS. Go to vertex mode and move the newly created edges so that the first two parts ar about the same size, and the last one is larger.
Select the three faces that now exist on this side and click the Bevel button and in Bevel Type, choose By Polygon so that it's extruding three separate segments instead of one large one.