I second a few of the posts about Shars. I personally own a benchtop mill, but I also purchased tooling with the bridgeports at school in mind.
My opinion...
Essential items:
1) Vise. Get a decent one but don't go crazy. You'll want a second down the road so you can buy the fancy Kurt then once you know what you want.
2) R8 collets. I agree ER chucks and Tormach TTS are nice, but until you need to spit out parts quickly, you can deal with changing the collet every time.
3) Parallels. Buy cheap ones. You'll probably drill into them a few times as you get going and you don't want to cry over expensive tooling.
4) Edge finder. Basic wiggle ones or a slightly more expensive electronic LED one is worth the extra few dollars in my mind.
5) Keyless drill chuck. I have 2, my shars one is very nice and very little runout. Buy the R8 to JT33 taper adapter too.
6) 115pc drill set. Buy a real cheap one and replace the drills with nice ones as you wear them out or find bad ones. I don't use many of them but I like having the full set so I have the correct tap drills.
7) Endmills. Buy HSS or look for used tooling sales. Avoid carbide until someone here has convinced you to switch. Your wallet starts crying when they break.
8) Dial or test indicator on magnetic Noga style base. Also a indicator holder for the spindle. You'll need to to tram your vise / locate hole centers. Shars has nice cheap ones. stick to .0005" or .001" (the .0001" will drive you loony)
9) One decent fine tooth single cut file.
10) Calipers. Here is one place I'd say buy a little nicer on. You want to trust your measurements and you will use them until they die (and price does equal lifetime when it comes to calipers)
11) You'll need way oil for you machine. Also WD40 works fine as cutting oil for aluminum, not as good on steel.
12) One of those 50 something T-slot clamping sets comes in handy as soon as you need to hold something not in the vise.
13) Center drill or spot drill, tap handle, taps, 5 flute 90* countersink (works for chamfering too), etc.
Have fun and remember you can always order more, don't go crazy at first. Everyone with all the fancy tools has accumulated them over decades, don't feel bad!