1/10/2017: Web site construction and or revision will be more expensive than you expected whether you have a company or do it yourself. It will take much longer than expected. It will cost you more than anticipated.
I have gone through 4 companies seeking an update. I paid several thousands of dollars just to learn that some did not do what they say.
So: If they say they can get right to your project that means you pay and they get right to cashing the check. The job may take 6-8 months to finish. Why? Because the take on more work than they can do now, so they remain busy.
If the company says the cannot start for 2 months that may be a worse delay. But maybe they are honest in predicting assigning your work to India.
If you go to a boiler plate type of company where they fill in your customizations to their form. How, it still will be a boiler plate with limitations.
The web site company will outsource your job to foreign language speaking programers which slows the process while you learn to understand the new language.
Advice: Spend more time in comparison shopping and getting assurances in writing with financial penalty for failure of on time delivery. This time spent will save time waiting for your product. Accept that you will pay penalty of learning experience. Education is not free.
Something Positive: Choose a company that uses Word Press. This gives you more choices thereafter. Certainly do not choose company that has proprietary site as you will locked in thereafter to them.
Finally: I like what I got after 18 months, 4 different tries and much money.