How do we get married?

[Preetmeester]

My girlfriend and I are looking to get married.
I am South African, she is British, but has been granted Irish citizenship. The options we have, as we see them, are to get married in the UK, Ireland, or South Africa, depending on the difficulty involved in each of these. My girlfriend teaches English in Asia , being married, we are hoping to get to travel together to Asia, or possibly, somewhere in Europe and settling in Ireland. I am currently living in Ireland on an expired visitor's visa and am undocumented.

We have done some research and to us, it would seem that getting married in South Africa would be the simplest, although, what rights we have and which EU countries might provide us with the least difficulty in attaining the ability to travel together, we are unsure of.
Is there any advice we might benefit from? And which visas should we be looking into?