Unless you are pouring the whole bottle into the recipe, you will probably want to buy a port that will repay some drinking, either while you're cooking or after the meal (perhaps with some stinky blue cheese?).
The two cheapest and tastiest ports that I know of are (1) Kopke's ruby port (around $13) or (2) Warre's Warrior (under $10).
Kopke's port is light, fruity and devoid of any sharp edges or bitterness. Very good if you are not sure you actually like port.
Warre's Warrior is a Reserve Port (or a Vintage Character Port), meaning that it has gotten a little bit more barrel aging and is thus more substantial. I'm drinking some as I write this, in fact. It's a little syrupy but also quite tasty in a fat-cherry-pie sort of way. It's got good spicy notes and a chocolatey finish. Remarkable for the price.
I've just written about some more Reserve Ports here, if you are interested...
re: Matthew Sullivan
I do agree with you on not using something that I am not likely to drink, just for cooking. For Port, I usually do the Sandeman's Founder's Reserve, or the Graham's 6 Grape. Both are decent Rubies, and the price point is not bad. I have several of the Kopke VP's, but have not tried their Ruby. I am not a big fan of Warrior, but that is just personal tastes.
I do the same with my red wine for cooking, using either the Ravenswood Vintner's Blend Zin, or the Peachy Canyon Incredible Red Zin-blend. Also, they do fine, should I have a glass, or two, while cooking, and the price does not break the Hunt bank. Both will hold up in the cellar for a few years, so I pick up a case of either, when they are on sale in PHX, and cook with them, plus drink a few sips, while standing over the range.
Unless the recipe, or my take on it, calls for something else (there is Port, then Port, then... ) I just use a bottle of less-expensive Ruby. How will the Port be incorporated into the recipe. I might move up the line a bit, if I am doing a reduction, without too much else, but then would probably stop short of an LBV, unless I plan on drinking it with the meal, or just afterwards.