Schmeky,
Yeah, you CAN clamp your work directly onto the mill table, to answer your question.
I don't mean to say that you won't need or want any of the equipment recommended for you here by these guys because everything mentioned has purposes in either making some things you may want to do possible or in making everything you do easier and more precise.
The clamping sets that are sold practically everywhere will handle all number of sizes and shapes of things once you get used to using them. In general one bolt, one T-nut, one straight piece, and one triangular piece make one clamp. The combinations available from your set are to clamp various heights of workpiece. The odd looking triangular pieces work with the straight pieces to form what's usually called a step clamp. Sometimes more than one of any of the pieces may be needed to build an effective clamping but usually one of each piece = one clamp.
The point is to clamp the work down firmly and straight down onto the table. This means that the straight pieces should be horizontal. The bolt through their hole and into the T-nut that fits in the grooves cut in the machine table. The stepped pieces are what brings the 'free' end of the straight piece up to horizontal. Think of it as being like building a bridge.
Make clamps TIGHT. This is part of why a vise is good for clamping. It's much faster and it can exert more pressure than you could put out using a one foot wrench.
I think that for a machine of this size 44-Henry is right in saying that most of your work will involve mills of 3/8" or smaller so just those collets will be enough for a while. Thing is that sets of R8 collets are almost always on sale so if you just get a set up to 3/4" or 1" you'll be set up and done with it.
The mill holders are more rigid than collets are but they also take away another inch of your work space. Always keep the amount of room an accessory takes between your spindle and your table. Just for fun take a 1/2" drill bit and put it in that chuck you have. As you start the bit into the chuck look at the space between the drill tip and your table - you'll see what I mean.
All the 'stuff ' seems kind of overwhelming right now, I'll bet. It'll get better. Just go slow and don't buy anything you're not sure you need. Keep reading and before long you'll be using the mill in the way you use a pocketknife - routine.
Here's a place that offers better prices on some of the stuff, in case you haven't found them yet:
http://www.cdcotools.com/
There's plenty of places to get tooling and I'd guess everybody gets their own set of favorites and I'm sure I don't know half of them. Enco is widely known and they have pretty good prices each month. They also have 'secret' codes that can give free shipping. You'll see the code posted in the first few days of most months in machining and welding forums. A lot of this tooling is pretty heavy so any break on shipping can help a lot.