Hi OP, I am an immigration lawyer, though of course anyone on the internet can say they are. I don't know all the facts of your case so I can't give you specific advice but I'll try to give you some helpful pointers.
Firstly, others on the board are quite right that you need to get yourself an immigration lawyer ASAP. Make sure it is a specialist with good reviews.
Second, from what I can see she tried to enter as a standard visitor, is that right? If she said she had come to marry you at the border then this will have triggered all this - you cannot enter the UK as a standard visitor if you intend to marry. She needs to either enter as a fiancée (if she intends to live in the UK afterwards) or as a visitor for marriage (if she doesn't) and she must have those visas in advance. The good thing is, if this is what the problem was then her honesty shouldn't be in any doubt as she honestly declared her intention and it shouldn't affect future trips if you seek proper advice on them and get help. Your representative can advise you on how she can get a copy of her Home Office file so you should be able to see what the notes of the interview say and respond to them in future applications if you need to. A good representative can help with this. If she lied or did not declare the full truth of the situation (lots of people panic and don't, please don't think I'm accusing her personally) then I would advise you even more strongly to seek specialist help - it may not be fatal to any applications but you will need advice.
Third, in order to live here permanently with her you will need an annual income of at least £18,600 per year, or savings of £62,500. The two can be combined if your savings are more than £16,000. These levels may be higher if there are any dependant non British children. If the income is from employment you must have held the job for at least six months. You need evidence of the finances. This can get complicated and you need a specialist's advice. The rules are rigid and it is generally difficult to rely on prospective income or third party support. Having said that, there was recently a case in the Supreme Court called MM (Lebanon) where the Supreme Court upheld the financial requirements but said that they did not fully reflect the UK's human rights obligations. Basically this means that there is now some discretion in the Immigration Rules and Home Office policy guidance but the change is only a couple of months old so you will need a good lawyer to help you through this if you need to rely on the discretion. There are othe requirements as well but this is generally the one people struggle with.
Fourth, she can't work on a fiancée visa, it will only be valid for six months and you must marry in that time, then she must switch to a spouse visa if she wants to remain here. This means paying a whole new visa fee and making a new application so it may be cheaper to marry in Canada or another country - I don't know where permits this or where is cheapest I'm afraid.
Fifth, others are right in bringing up the UK Ancestry visa - if she has a grandparent born in the UK (or Ireland if pre 31/3/1922) then she may be able to get this type of visa. It is cheaper and relatively easy. How old is she? If she is under 31 she may be able to get a Youth Mobility Scheme visa which would be valid for two years and allow her to live and work in the UK. She could then switch in country to being your unmarried partner or spouse when you met the requirements. If she is eligible for either of these routes then Ancestry would normally be preferable as she could settle permanently here quicker.
The fees calculator is here: www.gov.uk/visa-fees. A fiancée visa comes under 'settlement'.
Good luck.