Sure, you can use a regular DVR, but I don't know right now if it has component outputs for video. I'll check and edit this. And yes, you can certainly hook the sound up to external speakers. I do it myself.
Edit: Ok, I had time to check what they offer as far as the "regular" standard definition DVR goes. It's the "Explorer 8000". Note that there are Explorer 8000HD and 8300HD DVR models. I'm referring to the non-HD Explorer 8000.
This DVR does NOT have component video output. It does have 'composite" video and "s-video" outputs. Of those two choices, the "s-video" is your best option to connect to the Westinghouse. Youwill need to get an s-video cable if you don't have one. These are very inexpensive online, but you can probably also get one fairly cheap at a radio shack or best buy, circuit city, etc.
I have to tell you, though, that your Westinghouse will look much better if you're able to tune into the HDTV output that only an HD Cable Box or HD DVR can provide, not only from a tuner standpoint, but also from the available video outputs. Component video is by far the better choice between composite, s-video, and component. That's the order of quality as far as video goes., composite (the yellow single-cable jack) , s-video (black jack with several pin holes) and component (three separate color cables, red, blue, and green) Only HDMI/DVI would surpass component as an option, but your Westinghouse 22" doesn't appear to have an HDMI input, from what I could see.
(Edit: Your Westinghouse DOES have a DVI input, which means that if you got the HD DVR, you could utilize an HDMI-to-DVI cable to connect your video. You would still need to connect separate audio cables. The HD Cable Box (vs. the HD DVR) does not have an HDMI output, only component. To keep it simple, though, I would just go the component cable route, as both the HD Cable Box and HD DVR box will have component video outputs).
Note: On your Westinghouse, the component inputs are labeled YPbPr, but you will see that each jack is color coded. Just match the red to red, blue to blue, and green to green.
Also, be advised that switching to an HD cable box from Time Warner will NOT cost you any more money, unless you're only getting the very basic cable service now. You will have to have at least their standard digital cable service and then just tell them you have an HDTV set and need the HD cable box mentioned in the previous post.
What WILL cost you extra is if you get the DVR, whether it's HD or non-HD. You will be charged the standard fee for a cable box, PLUS the fee for "DVR Service", which is probably 9 bucks or so. Again, if you get the standard DVR and later upgrade to the HD DVR, it won't cost you extra. It's just a one for one swap.
So, you have some choices to make. If it's absolutely imperative to record TV now on this set, then your only option is to get the the standard DVR (or Tivo or even an HD Tivo). I haven't mentioned setting up a pc based home theater because you didn't say that was something you were interested in, so I'm sticking to just regular TV options from the cable company.
Just remember that your viewing experience will be much better on either an HD cable box or HD DVR, as all you will get on the standard DVR and/or standard cable box is regular SD tv, and lesser-quality video outputs.
Here's a link to the standard DVR. You will see on the back panel diagram (expand the pdf file above 100 percent and scroll to the diagram) the s-video output connector, and the standard stereo RCA jacks (red and white), as well as the digital audio output jack.
PM me if you get this equipment and have trouble setting it up or getting audio, etc.