Really really REALLY consider marrying in the USA first and then applying directly for a spouse visa. No one has to know. You can still do the big white song and dance thing in the UK afterwards but save a boat ton of money and visas.
For either the fiance or spouse visa: You'll need to move to the UK and obtain a job that allows you to meet the income requirement (£18,600 annual minimum earnings). If you have a job currently in Ireland that meets this requirement, you just need to prove you have a job offer and are starting in your new role in the UK within the next 90 days.
If you do not currently meet the financial requirement with your employment in Ireland, you will need six FULL payslips from your new employer in the UK. This will likely mean working there for 7 or 8 months before you qualify to sponsor your partner.
Once you meet the requirement to sponsor your partner:
You collect all the paperwork (6 FULL months payslips, none dropping below £1550 per month. 6 FULL bank statements showing all deposits from your employer, a letter from your employer (details can be found in the guidance), a copy of your lease and a letter from your landlord stating your partner can live with you once the visa is granted (or mortgage statement and land registry if you own), and proof of your relationship. There is no medical exam.
If your partner comes over as a fiance, you will have the following:
receive visa (valid for 6 months)
arrange partner to move to UK
Get partner on council tax bill showing they are now living in the UK
make appointment with registry office
give notice to marry (partner must have been in the UK for at least 7 days before you can give notice)
wait between 28 and 70 days for the Home Office to grant permission for the marriage
marry
apply for the next visa FLR(M) before the 6 month fiance visa expires
During that time, your partner CANNOT: Use the NHS (must pay for any and all services, even if the GP insists its no charge - major headache), Work (even remotely for their US employer), volunteer
If you decide to marry in the USA first, you eliminate all that legal giving notice non-sense and can actually plan a DATE to marry - something you can't do with the fiance visa. Also your partner can work and use the NHS from day one.
Fees are:
Fiance visa:
£1,523
FLR(M) after 6 months: £1,033
NHS levy: £1,000
Spouse visa:
£1,523
NHS levy: £1,000
So you save just over £1000 currently by choosing the spouse visa over the fiance visa and get a teeny tiny bit of the romance of getting married back in your lives.
Non-priority visas typically take 60 working days to process (12 weeks). Priority (an extra £573) typically take 30 working days to process (6 weeks).
Best of luck. MARRY FIRST!!!