I am looking for some immigration advice – hopefully someone here can help me

I am a British citizen and my girlfriend is from Chile. We are currently together in the UK; however, she entered the country on a visitor visa that will expire in about three months.
She would like to live permanently with me in the UK. We don’t meet the conditions for the partner visa and so it seems that the only option is for us to get married. (It’s slightly sooner than we would’ve otherwise planned it... but she’s a keeper so it’s all good

My main question is this: does it make more sense to get married in the UK or in Chile?
(If I understand correctly…) if we get married in the UK, she needs to leave the country, apply for a marriage visitor visa whilst overseas, return on that visa, then we get married here, then once married she can apply for a family visa which allows her to stay longer. Is that right?
However, if we were to get married in Chile, I can get married to her on a standard tourist visa, so that saves us the time and hassle and applying for a marriage visitor visa. However, we would still need to apply for a family visa in order for her to stay in the UK – would it be more complicated applying for a family visa if we get married overseas? Or is the process of applying for the family visa pretty much the same regardless of where the actual marriage takes places?
And if we get married overseas, does she apply for the family visa whilst overseas? If not, on what kind of visa could she come into the UK and then switch to a family visa? (According to the gov website, it is possible - and cheaper - to apply for a family visa whilst already in the UK)
Any help would be very greatly appreciated!
We have done a lot of searching online but the information we have found on the official sites has not been able to answer our specific questions…
Thank you
Tom