|Wireless Router? - Yes|
Wireless Access Point? - If you already have a router that isn't wireless capable, you could go with using an access point. If you don't already have a router, then you'd get a wireless router since an AP can't do NAT or DHCP.
If you already have a non-wireless router, I would compare the cost of a wireless router as versus an access point. In my experience, the router is actually less expensive than the AP. If you can find a good wireless router for less $$$ than an AP, definitely get the router.
Wireless Adapter? - Does the PS3 come with a wireless adapter? I have no idea. If it doesn't, then yes, you'll need one.
Will N be better than G? - Yes and no. Yes, it can, and does, provide more bandwidth than G. Wireless is still wireless and wireless sucks in comparison to a wired solution so that's why I added the "no" since both N and G suck totally when compared with a wired solution.
In all honesty, it shouldn't matter in the long run. I would get N and ensure whatever you buy is backward compatible to G (most likely will be) because your PS3 may already have a wireless adapter that's G. In the end, it's not likely to save you any $$$ to go with a G router/AP so you'll probably want to go with N. This would be handy for use with modern laptops and PC's with N adapters.
Is this going to work without aggravation? - ROFLMAO. Are you an optimist? Is your glass always "half full"?
Chances are it won't be without aggravation..........we are talking about wireless and wireless is inherently insecure, subject to lag and latency issues, and, is harder to setup/configure than wired solutions. However, if you're reasonably intelligent, have some experience with computers and networking, you should be able to get it setup and working. I suspect if you did some googling with regard to connecting your PS3 to a wireless network you'd find some tutorials and guides.
NOTE: If you buy a wireless router and already have a non-wireless router connected to your internet you'll want to click on my name above in my response and read my "how-to" guide on "adding a second router". You'll want to pay attention to the scenario where you connect "LAN port to LAN port"
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.