I lead the VegasTechFund to become the 5th most active Micro VC firm. I'm currently an Indie.vc scout, an active early-stage investor, founder @ Data Science Alliance.
I help startup community builders understand how to lead a more tightly unified community through the ESHIP principles developed by the Kaufmann Foundation.
When bringing in a new cofounder it's important to give them an opportunity to earn their equity. Typically this means a vesting schedule over a certain period of time. For example you may decide on an opportunity to earn 10% of the company over 4 years with a 1 year cliff. This means there is no equity earned for the first year. After the first year they would immediately receive 2.5% (for the previous years work) and then a prorated amount (.2%) each month after until the end of the fourth year. This helps everyone's incentive stay aligned.
Now, in your situation it's important to understand why you want a CTO cofounder. From your description it sounds like you already have everything you need. Think about this first.
If you still want to find a tech cofounder then consider the following when making an offer:
What you would want if you were them?
What are they giving up to join you?
What will build a long term relationship?
What is the company worth without them?
The amount of equity can be supplemented by a salary, amount of time committed, or other compensation. Without knowing the specifics it's very challenging to give an exact % answer.
A year would be a minimum amount of time. We all know that forecasts are guesses so, what's important is how you've determined the numbers. Of course the numbers need to show that the business is worth an investment.
The rational justification of the numbers to demonstrate your expertise in the market is the most important part. You need to tell a compelling story that's supported by the data you present.