For this I am not even going to pretend to know where to look to find stuff in your country, it should not be too hard to find anything I mention though.
Generally you have two main options for consoles and external devices.
Direct capture
Split capture
Direct is something like a capture card that you play on the screen with. The problem comes in that there might be a necessary latency (video processing is easy, video processing in real time is not) and that can kill your abilities when playing games. If you mainly play games where reaction time is not such an issue then that is an option. However this option is often quite cheap, I do suggest a proper PCI card though rather than too much fiddling with USB stuff (doable but it is obvious to everybody that knows).
Split capture involves you either have a device that passes video through and onto something else or a device that splits the video output so you can have a normal video out to play on and a recording machine.
Video cameras with input... I am assuming you are going to want to do this on a halfway modern console so you are then going to need HDMI/DVI, component at the very least and probably everything from RCA down through RF for the older consoles (though emulation is always an option there). I assume you will just get one of those "splitters"* if you brush up against HDCP, I am not sure what goes right not for normal gameplay (films are different of course) and consoles but you should be OK for most things. RCA and lower level component is doable in consumer world on a camera, I have not really seen anything I can point at and say "that" for big boy component and HDMI.
*check but often if you see a Chinese HDMI splitter on ebay or something it will probably also have the HCDP master keys in there ready to strip things out for you, naturally ebay does not like this so you may have to read between the lines.
These days there is also the "direct to youtube/twitch/whatever" stuff. I would not dream of putting unedited and unscripted game footage out there for public viewing but others are not so worried. From what I have seen and heard the live streaming/capture apis they have would make a video engineer cry (though live there is a different matter) and also seriously trouble the consumer end stuff aimed at people with a clue (prosumer if you will). That said though I am by no means an old hand at video I have been doing it for a while and tried to learn the "old hand" ways of doing things; beware the cranky old man basically, of course there is no school like the old school (even if my definition of old school involves digital video and non linear editing).
Capturing then, three main options once you have decided how you are going to play it.
Camcorder. I already went but to go again if you had one already that could do it then I might have a hard time selling you on another. I would not do it as a main thing unless you were also interested in capturing things on a camera and were on a really tight budget. If you just want your mug on screen as a small reaction box or talking heads intro segment then a decent webcam with some halfway nice lighting should do for the time being.
Dedicated box. For a while a lot of people used DVRs of various forms, Hauppage did fairly well out of this. Today the "I want to be a youtube cretin" market is apparently big enough to warrant the attention of device manufacturers, though most are aimed more at the PC but with proper encoders (see note in a moment) rather than nasty basic USB stuff that is basically a half nice webcam grade of footage (though more than acceptable for a lot of "SD" stuff). Roxio and Elgato are probably the bigger names here though Hauppage is still doing good stuff.
PC. Obvious really. Hauppage once more will come first to do what you want as far as a PCI card goes, keep on your toes though as a lot of things are aimed at TV decoding and might lack a bit. I already mentioned several times the basic USB stuff but if you do want external then firewire does provide you with some options that I will not sniff at.
Footage quality... a lot of these will claim to come with "hardware H264 encoders" and they do. In the game world I have not seen something that will stack up against X264 on a normal day but that is OK as you can just set the size up a bit (assuming you are not live streaming) and by the time is being played back after it has been recoded by the web video people it is going to be the same.
After this.... if you are twisting more towards live streaming, editing and uploading in real time and other such things I hope you have a decent wallet. Assuming you have audio equipment worth mentioning (and I would have some nice stuff here, probably even as a priority over truly nice capture equipement) then Blackmagic Design (usually their ATEM line) are the brand that do a lot of good stuff, I have to look more into it but they are competitive with Hauppage for capture cards of the required feature set too if a quick scan of their website is anything to go by.
