Hi, You can immediately work with a spouse visa. You will need to apply for NI number (National Insurance) & a Bank Account. The next step before your spouse visa expire is apply for Permanent Residence. I'm not sure how long a spouse visa is valid these days. Mine was 2 years. So a month or two before it expires you will need to apply for Permanent Resident. Be sure you have money in the bank (£3000) should be enough I'm guessing. You will also need to Pass the Life in the UK test & any other test that is required before applying so leave ample time to prepare & pass the exam before applying. Being employed will also help to have a favorable decision.
After the required number of years (depending on the rules now) you can apply for British Citizenship.
Just to give you an overview of the time frame I had.
Spouse Visa 2 Years
Permanent Resident 1 Year
Then I was able to apply for Citizenship after.
Hope this helps.