First off, welcome to the wonderful world of being on the water! I am a relatively new kayaker myself, only being at it for about 2 years now. I have a collapsible one myself, that I can easily pack in my jeep.
As for tandem, I am not sure if there are specifics to different paddles. From my experience, and what I've read, you want a paddle that isnt too long (dont go to extremes either way), and you are looking for a touring paddle. A flat blade will likely work best for you (the paddles themselves will be curved, but the edge of the blade is flat). I dont recall the model I have, but it is an aluminum shaft, plastic blades, and comes apart in the middle via a button/hole configuration. I can also feather the paddle, which means I offset one of the blades when the paddle is put together. This is only if you are heading into a strong wind-as I am still a novice, I never feather the paddles-havent yet had the need.
PFDs, what I use is a vest with pockets-its designed for fishermen, and has a few nice pockets to put a PSK, knife, flashlight, etc in it. Also a nice place to attach a whistle. I recommend one of those. They also make PFDs specific to kayaks, with flotation cut away on the back bottom half, to aid in sitting in it.
Two other recommendations, though not necessary, would be a deck back, and spray skirts. Deck bags allow for conventient access to items like food, water, a camera, compass, etc-all right in front of you. A spray skirt could be a later purchase, but it prevents water from entering the cockpit, particularly in rough waters.
Some other things would be a bilge pump, and a sponge. when a kayak gets swamped, you will need to get the majority of the water out. And, its a cool water cannon
. The sponge is simply to sop up water-not a necessity, but certainly nice.
Budgeting, go with the necessities first-paddles & PFDs. And, pick up a book. I got one a few years ago, "Kayaking, a Trailside Guide", that is pretty thorough. I learned a lot from the book. I do flatwater only, so I dont need to learn eskimo rolls, and the like-if I am doing that, I am in SERIOUS trouble. but, its a good idea to practice dumping the yak, and getting back in.
Lastly, have fun. There are FAR more experienced paddlers here, that I am sure will chime in. But, its all about getting out on the water. Have fun with it!