First timer needing some help!

[stinkyattic]

I like you already... you put your questions in the easiest format to answer, so I'll answer them!

1. For two plants, what would be the best light to use with the most efficient light output per wattage?

If you want your e-bill to stay about the same, and not have to also worry about adding a cooling system, flourescents are excellent.
In fact, they are the BEST thing for seedlings, and you can veg under them just fine.
Since you are only planning on 2 plants, and you're a newb, can I suggest you start at least 8 seeds? If I were you, I'd do 4 plants. Then even if 3 turn out male you still get one left over for bud.
That number of plants will be fine for the smallest HPS you really want to bother with, which is a 250.
And a HPS really IS pretty important for flowering. Some people have done flouros the whole way, but do yourself a favor and get a little HPS to finish with. You can still supplement it with fourescent side lighting if you want.
But a 250 is not going to make your e bill noticeably higher, especially if you do other things around the apartment to conserve energy.

2. What is the best, most cost-effective way of filtering the air out of my cabinet? Would the air be clean enough to let out into my room? Should I run it out the window or into an exhaust vent? I live in an apartment so I don't know where the exhast vents run out to.!

You can build a little home-made carbon scrubber, plans are around the site if you dig. Or you can go the ozone route. I don't filter or treat my exhaust, but if certain friends who would recognize the smell of ripening cannabis come over, I keep a can of Ozium handy and it is effective. They make automatic can dispensers too. Also hunt around hydro supply websites and look for the air handling sections.

3. Should I consider using shielding material to avoid being caught by infrared cameras or is my grow small enough to avoid suspicion?!

Naw. The only shielding material you want is a small piece of duct tape over your mouth. That's a small grow. Just hush.

4. What precautions do I need to take when drying my plants? Should I be worried about odors with such a small harvest? What cost-effective methods are there to dry without creating a lot of smell?
!

I assume you're not perpetual-cropping, so when you take your plants down just hang them in your grow space and keep your odor control system going. No worries.

Good luck