I need to convert my old VHS Tapes to ... Files? DVD's? HDV tapes?

The most important thing isn't which digital format you use -- but to get the conversion done.    Analog tapes degrade with time ... and the longer you wait, the more degraded they will be.    Once you have the content stored in a digital format, there won't be any further degradation.

The easiest way to convert is to buy a VHS -> DVD recorder ... something like this:
http://www.amazon.com/Toshiba-DVR670-DVR670KU-Recorder-Built/dp/B001TOD3KU/ref=sr_1_1?ie=UTF8&qid=1347744191&sr=8-1&keywords=toshiba+dr620+dvd+recorder+vcr+combo+dvr620

... you then just insert a tape;  insert a blank DVD-R;  and start the copy.    Once you have all of the recordings on DVDs, then you can easily copy the DVDs to a hard drive;  do any editing you want with any of the various video editing packages designed for that;  convert the format if you choose; etc.    And you'll have a DVD with the original safely preserved in a non-degrading digital format.

Note that if the quantity of tapes involved isn't very large, there are service companies that will do this for you -- and are set up to let you view the digitized tapes before they burn the DVDs and select just what you want saved.   e.g. http://www.imemories.com/microsite/transfer/vhs/

... you can do the same thing by using a dedicated capture card and recording directly to your PC's hard drive;  then using an authoring program to edit the videos and create the DVD master; etc.   But this can be somewhat intimidating if you're only doing a few ... and there's a fairly steep "learning curve" to do a really good job of it.    So I'd suggest either using a service;  or just doing a straight tape-DVD dub using a recorder like the Toshiba I suggested above.

If you have VHS Cassette Player + Video Out RF Cable + TV Tuner (Built In) Card (eg. Pinnacle or Pixelview)

Now get the TV Tuner Card installed to your PC via PCI Slot. Connect the VHS Cassette Player with the help of RF Cable to the TV Tuner Card TV/Video In.

Now you simply have to start the play back from the Cassete Player and then use the Recorder software bundled with the TV Tuner Card to record the inputs from Cassette Player. Here I would suggest to convert/save videos in AVI File, but mostly it will be available in MpEG format. So you can use any simple Video Converting software to convert in AVI format.

Now a days no one use VHS Tapes, so if you do not have above better than buying new hardware check out if someone already have the VHS Cassette player. TV Tuner will be useful for recording inputs from TV Channels also so it will be useful in future also but not VHS Cassette Player. Hope you getting my point.

Hope this helps !!!!!