With regards to visas, your main hurdle will be getting a visitor visa for attending the part of the recruitment process that happens in the UK. These are handled exactly as anyone else who wants a visitor visa to attend a job interview; the army does not get any special preference.
In order to get this, you need to convince the ECO of three things:
1) That you actually have a job interview to attend. (Papers from the army should do this for you; at least there will be no doubt whether your potential employer is itself legit).
2) That you can afford to eat, sleep, etc. during your trip.
3) That you will go back to Ghana after your trip.
Having your father sponsor the trip may in some circumstances make it easier for you to do the second of these, but won't help at all with the third one. On the contrary, just having a father who lives in the UK will make the third task very difficult for you.
You'll need to demonstrate a reason that makes you absolutely need to be present in Ghana after your trip. From your description it sounds like you don't have such a need, and if that is the case it will be somewhere between extremely difficult and impossible for you to qualify for a visa.
Sorry, but them's the breaks.
The Visitor Rules are in Appendix V of the Immigration Rules
