I am trying to find what pcb connectors that are best used and available.

Firstly I want to connect a 800 mAth ni-ion battery pack to a pcb with a suitable socket and plug.

Secondly I want a suitable mains plug and socket for a maximum of 1 amp. That can be connected into a plastic housing.

Lastly a suitable pcb mount socket that can also be secured to the plastic housing and then a plug

 

Search Digikey for Barrel Connectors for the battery.
The mains plug would be a type available to where you are located, unless you want to use, and have the N.A. style?
Max.

 

For battery connections, I use MPA-100 style connectors (not just TE), with orientation but no lock. Here's the female: http://www.digikey.com/product-search/en?KeyWords=WM2000-nd&WT.z_header=search_go

For connection to the outside world, I use a barrel power connector like Max mentioned. I prefer the switched connectors. The ring connection is switched. You can use that to isolate the battery from the rest of the circuit for charging, or in very small designs, I use it as the on/off switch too. With plug installed, it is off. With plug removed, it is on.

John

 

For mains connection I wouldn't sidetrack from the IEC standard plugs that "everyone" expects to find in products these days. You can find them as panel mount or pcb mount, they are cheap and you have a cable for it already laying around. Either these or solder wires directly to the PCB using cables glands to feed through the enclosure. I think you can also buy power cords where the pigtail end have a moulded strain relief that fits in a slot you make in you enclosure.
Look at C5/C6, C7/C8 and C13/C14
http://en.wikipedia.org/wiki/IEC_60320