The FAQ section has information on visas, including a UK EEA Family Permit.

Requirements:
The EU citizen intends to exercise their Treaty rights in the UK (employment, self-employment, study, self-sufficient, etc)
The couple must be legally married to each other / in a civil partnership with each other
They must have met each other
They must intend to live together
The couple must be traveling to the UK together or the EU citizen should already be in the UK

The EEA Family Permit would be issued for 6 months and allows unrestricted employment in the UK for that time. During those 6 months, it is expected the EU citizen would apply for a Residence Permit and their spouse/partner applies at the same time for a Five Year Family Permit.

It appears you should have no trouble qualifying. You should contact the embassy about your specific case for the most pertinent information. Anyone else been through the process? Best of luck!

 

Your job offer is dependent on you being able to get to the UK and accept it and sign the contract. Your eligibility to work stems from the fact that you are married to an EEA National.

Now in getting your EEA Family Permit (Which I assume you will be applying for while in your country of current residence), your financial proof would be existing bank accounts and/ore your current employment there. You can definitely add the offer letter from the UK as further proof that you will not be a burden on the UK Government once here.

In your application your wife can state the she will be self sufficient "for the moment" as the income derived from your job offer would sustain you both. It would greatly help your household income though if she also eventually got a job as living in the UK (specially in London) is quite expensive.

Best of luck, and post additional questions in your thread or share your experience once you complete the whole process.

 

It will not be seen as you trying to cheat the process, as you are entitled to work anywhere in the EU. The family permit is actually just a formality and to ensure ignorant airline and border officers who are not familiar with the EU Directive 2004/38/EC will not turn you away at the border for not having a "visa" - though technically you don't need one.

As for your residency when you come here, it would be wise to stay with a friend, even for a few days, so you can go around and look for a more permanent arrangement and view houses, flats, etc. Staying in a hotel is cost prohibitive, not to mention the Home Office will see your financial statements to verify you can indeed stay in hotels for awhile as you're looking for a place to live.

 

A letter from your employer outlining them sponsoring the hotel costs, and you having a cover letter mentioning this would greatly help your application.