If you're not bothered about opening up your computer (and there's very few people that should be in this day and age!) then the PCI card is the way forward. Tucks out of the way, easy to install and generally more reliable than the USB alternatives. I'd only recommend the USB route over the above if you've really got a very good reason why you don't want to open your computer up!
As far as I'm concerned, those are the only two realistic choices. Don't really agree with that video to be honest, it's massively over complicating things. If you're in the position to be considering using a specialist choice then you'd have the knowledge to start with and wouldn't need to watch the thing!
As for the other methods - well I don't count "having it built in" as a method, since that's not a way of making a desktop wireless... bad choice of explanation there in my opinion. PCMCIA card / air card / whatever - almost always a stupid choice on desktops. Generally more expensive, rarely supported - I wouldn't really count that as an option in the vast majority of cases. As for an access point, again I think it was a bit silly to mention those and as such wouldn't count them, they don't make your desktop PC wireless per se, they add a wireless point of access (hence the name) to your network. As the guy said, they have the advantage of potentially being the fastest and having the best range. But any decent PCI card should be able to perform at the same level and I can think of LOTS of disadvantages:
- They might not even work since that's not how they're really designed to be used
- They require an extra power supply, hardly good for portability
- They take up a lot of space
- They're the most expensive option
- They take up the ethernet port on the back of your PC so if you want to make a cabled connection as well (and don't have dual ports) tough luck...
- They allow an attacker a direct line of communication into your PC without having to go through the "main network" first
WAPs are great in lots of situations, but this is not one of them!
Only other thing I'd throw in (which is in my mind something else the video missed) is to ask why you want to go wireless? Desktops usually stay in one place, and if you've already got a cable going there then it seems silly to switch. In fact I'd even recommend running some CAT5 if it's not already there, it's cheap, faster than wireless, more secure than wireless, more reliable than wireless... you get the picture
With laptops that are constantly moved around I can understand it far more, but with desktops, cabled is almost always the better option from a technical perspective.