Hi sarah, sounds like you have a fun project ahead of you
It has been asked and really is key, are you wanting to integrate a turntable into an existing audio system in your living room, or are you wanting to get the audio off the vinyl and make an playable audio CD, create mp3 files to listen to on your PC, Mac, Linux... system? If it's a computer it will help to know the OS (type of computer).
I personally wouldn't bother with the first, too cumbersome any more, too expensive to maintain - needles (stylus), turntable adjustments, space. It's up to you though, no right or wrong here

I would spend as much as I could on the best hardware available.
If I was you, I would get the audio off your cherished vinyl, save it to a lossless format (.wav file) to save as the master copy, and set your vinyl aside. Your newly created wav file can be edited for free with software to remove those nasty pops and clicks, and then encoded (saved) to better and smaller files and remain lossless (bit for bit copy of original) using flac format, or a lossy (not bit for bit exact but human ears cannot hear any difference - despite what they say) format like mp3.
Getting the audio off the vinyl and onto your PC is where you need to start. Here's a few links to the basics...
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http://www.turntablelab.com/pages/beginners-guide-to-turntables
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http://www.turntablelab.com/pages/recording-vinyl-into-your-computer-guide
I would do a few searches for recording vinyl to computer and get a few more opinions, take a few notes, ask a few more questions, get your needed hardware, get it setup properly... and so on. This is really easy and should be relatively inexpensive if you go the record to computer route. Make sure you're reading the right articles... recording on a PC (Windows) versus Mac, etc.
Here's a few rules I follow, my way may not be best for you
... You don't need an expensive turntable, top of the line, but a good one that will last long enough to record what, 20, 30, 100 albums, then you put it back in its box - you've got your audio.
... Save (record) your vinyl to a lossless audio type, usually .wav on PC. Don't use the original .wav, make a copy and edit the copy in case you make permanent mistakes. If so, simply highlight and Copy a new editable file to try again. When using lossless digital audio, the 100th COPY is as good as the first - assuming your PC is in good working order, bad RAM or bad hard drives can create an imperfect copy but this rare. I would save the original (Masters) in one folder, clearly marked, and only copy over to a .\Working folder where the editing takes place.
... Get 2 needles if possible of decent quality, have a backup.
... Use a test album to help you get your setup working, volume, levels, etc - don't use your vinyl - each playback it degrades a bit. Try to get the recording figured out so you can get your master digital copy the first time, in 1 play when recording your albums.
... Clean but don't scrub the vinyl, to get any buildup off the record before recording - helps with sound and the life of the needle.
... Use good headphones for recording and editing to get the sound as close to your ears as possible (loud is not what your after, but removal of extraneus noise). External speakers are OK, monitors are a bit better but should be near-field (close, directed sound) to you. This is purely preference, we all hear the same source a bit different - if you like it then it is perfect.
... You don't need to over process the files, usually pop&click removal, mild volume control, a few other things will create a really nice finished copy.
I posted alot, sorry for my rambling, this was a hobby of mine at one time, saving old cassettes & vinyl to digital, just hopin' you get it exactly as you want it. Its a bit of work, but when done you will have a copy that will (should) last longer than you will
Mike