The best (and cheapest) option is to actually get a dedicated hardware recorder, like a PVR. Haupage probably makes the best ones around for the price. Don't expect HDMI, because part of the HDCP standard is to not allow recording (it's for movie protection junk, which is stupid) ... but you can do up to 1080i through component.
They should really extend the HDCP standard to only disallow movies from being recorded ... not games. It's quite frustrating.
Also, most PVRs also work as hardware upscalers as well. So, if you set it to do this, it will upscale and output SD materials in whatever resolution set to, 720P, 1080i, whatever.
It will make a USB connection to the PC, where you can record all this stuff. I recommend something like LightWorks, it's a professional grade open source, free to use video editor (amongst other things). It will let you capture the stream as well as edit and put in effects and any overlays you might want.
And, the PVRs, honestly ... they're actually cheaper than HD capture cards ... so ... it really is the cheaper route and it has a lot of benefits (like not stressing the PC to render AND capture) And, I believe, because it's pre-processing the video stream, you could do live streams with it if you wanted. But I'm not sure.
This is what I'd, personally aim at. As for models, just take a look around see what fits your price range and look up review and even examples (on youtube or something) to see if it's the quality you want.
Video capture on handhelds is usually not possible unless you do some system modding. Most people get around it by making a mount for the system and fixing cameras on the unit. The handheld systems that can be played on a TV (like GBA though the GameBoy Advance Player) can be captured through the same means as any other console. Very few handhelds will have output cables. But they do exist, they just weren't meant for consumer use. As a result, they're rather expensive.
Last edited by Crono on Wed Jul 11, 2012 2:59 pm, edited 1 time in total.