Installing rings

My ceiling is 10 feet high. Can you recommend the best anchors and strap length that I should go for?

Strap length: go with the 16*

 

Anchoring: This depends on what type of ceiling you have, dry wall and joists or concrete.

 

For Concrete, Use standard Concrete Anchors with Eye Bolt inserts

 

For Joists: Run a 2x4 across 3 joists and either a lag screw with and eye end or a through bold with eyebolt end.

 

Standard spacing between the rings is 50cm (apx. 19.5 inches)

Another option may exist if you have exposed joists and beams.  I have an exposed beam (I mean a thick piece of wood or metal), you may be able to rig an anchor with nylon straps, such as are used in rock climbing.  I did this in my garage, which has a very solid beam going across the middle.  I have not tried to rig anything on the joists; the load would need to be spread somehow, I think, as indicated above.

 

If you end up using eye bolts, purchase ones that are a solid circle all the way around.  Many eyebolts at the hardware store are incomplete circles of metal, and are less effective at holding a load.  

Great point about the eyebolts, then need to be cast or welded shut.

I got my rings and I have a 2 x 6 across my ceiling joists that I will put the eye bolts in. Can I put the straps throught the eye bolts, or do I have to use carabiners? 

I would definitely recommend carabiners.

In choosing carabiners, you may have a choice between aluminum and steel.  Many carabiners designed for rock climbing are lighter, as they must be carried, but may not be as strong or long-lasting as steel.  Both will hold you, but there is no need to spend more for a lighter weight.  Also, there are different "gate" options, such as threaded gates with a nut, or a spring gate.  (or there are spring gates with a locking nut)  Unless speed is needed, the threaded carabiners may be more secure.