If your wife only intends to spend a short time in the UK to determine whether she likes it here, then a Spouse Settlement visa wouldn't be appropriate.
She could apply for a visitor visa which will allow her no longer than 6 months in the UK. However, she would have to submit evidence of strong ties to the US, e.g employment, property ownership, study, family etc in order to convince the Entry Clearance Officer that she won't overstay her visa. This may be difficult when you (her husband) are living in the UK. Entering as a non-visa national isn't advisable as she would still need to carry with her the same evidence that would have been submitted in a visa application, to enable the Immigration Officer at Border Control to make a decision on entry.
It would also be wise to ask for less than 6 months in the initial visitor visa application.
The Spouse Settlement visa application requires documented evidence of your ability as her sponsor to meet the minimum annual income level of £18,600.
Without earnings you would need £62,500 in savings, held in an accessible account for a minimum of 6 months. These can be joint savings. Proof of a genuine relationship and adequate accommodation is also mandatory. The visa fee will rise on April 6th to £1,195 (currently £956). The route to permanent settlement is 5 years, (2.5 years + 2.5 years). After Indefinite Leave to Remain (ILR) is granted after the 5 year period, if she is married to you as a British Citizen she would then qualify for BC, assuming she meets all the standard requirements. There is no shorter route.
If applying for a Spouse visa, she will also have to pay the NHS Surcharge of £600 online before submitting her visa application.
Additional visa fees are required at each stage of the 5 year settlement process.
Bear in mind that it isn't possible to switch to a Spouse visa (or any other category of visa) from within the UK while your wife is here as a visitor.
https://www.gov.uk/join-family-in-uk/overview
I've moved your post to the correct forum.