Can you be more specific about what you are trying to do? What components do you have? DVD player, HD DVD player, VCR, HTPC, etc? This will help us understand what sources you have, what resolutions they are, and why you want to upscale/upconvert.
Also, and probably the most important question, is why you feel you need upconversion. Typically upconversion is required when you have the capability to run only one cable to your TV. (or you have run out of connections on the TV and need the AVR to switch the inputs) This happens when you have a nice flat panel TV that is actually mounted on the wall, and you can only run a single cable to the TV. With upconversion, you can plug any source, analog or digital, and the AVR will convert the analog to digital, and scale the image to fit your output resolution, then it sends this signal over HDMI with the digital audio signal to the TV. As an example, you can plug in your video ipod to the AVR in your cabinet, and the AVR will convert that analog signal into a HDMI signal, and you can view your videos and photos on your flat panel hung on the wall without having to plug anything into it. Typically, the analog to digital conversion and upscaling are not as good as what your TV can do on its own had you plugged in the sources directly to the inputs on your TV. This is especially true for the budget receivers. Some high end receivers have high end conversion and scaling better than any TV but these are $1500 and up. So, the best way to get the best picture from various sources is to use the TV inputs for all video connections.
So, having said all this, from what I can tell about your setup, you have a HTPC that plays nearly all your media. I don't see any reason why you would need upconversion unless you have run out of inputs because you have every game console known to man. From what I can tell, you are using the analog Component from your HTPC and you want to convert it to HDMI. Why not just get a DVI to HDMI cable and run HDMI from your HTPC directly to your TV? DVI and HDMI are the same signals, except DVI does not carry audio. There is really nothing wrong with Component Video, and just converting it to HDMI after it is already component will actually hurt your picture quality, not help it. Component is perfectly capable of running high resolution at very high quality, and HDMI is barely a step up if at all. If there is anything i am missing just let me know.
I am also really confused about this comment: "I have a media PC which I use for watching DVDs on my big screen with. I thought I could "out" the component video from there to my AVR and from there to my TV via HDMI...I guess that would require both an upscaler (for 480p to 720p) and an upconverter (component to HDMI)" You are correct that if you output 480p analog you will need upscaling to 720p analog, and conversion to 720p digital, but why are you running your HTPC at 480p resolution? What kind of TV are you using? What is the native resolution of that TV? You should set your HTPC to the exact resolution of the TV. If it is a 720p TV, set the HTPC to 1280x720, if it is a 1080p TV ( am assuming this is the case because you want a AVR that can do 1080p upconversion), set the HTPC to 1920x1080. The HTPC can do very good DVD scaling, depending on the setup of your HTPC.