Not to get overly mathematical, but there's a formula that you might be able to use as a starting point. If "X" is the average outcome for the company with the addition of this friend of yours, then he is worth "Y" such that X = 1/(1 - Y). For the company, this translates into Y = (X - 1)/X.
In your case, if you feel that his tenure and contribution would increase the average outcome of the whole company by 20% ("X"), then Y is (1.2 - 1)/1.2 = .167. So you'd break even if you trade 16.7% of the company's equity for him.
It's very difficult to make any assessment without knowing whether he is being brought in as a co-founder and whether he's being compensated financially. If he is for both, then you should up the ante. If you are recruiting him as one of the first employees, a different set of rules governs. Generally, you try to strike a balance between his compensation and his equity. Higher compensation means lesser risk, which yields lower equity (and vice versa).
"Standard" vesting is 4-year vest with 1 year cliff, as Nick has succinctly stated. I would not recommend deviating from this standard unless you have a reasonable justification.
As a side note, most early-stage startups do not go out and recruit COO. Hiring an experienced, full-time COO may cost you more than you pay yourself. Are you willing to make the financial sacrifice? Can you realistically forecast additional revenues you'll gain from the decision? Put another way, will hiring the COO free up enough of your time that you can focus on generating additional sales or raising capital for the company? Or will product quality improve as a result of the new COO that will in turn improve client retention and repeat business? Maybe that you are better able to control costs because the new COO will be accountable to do so? If your responses contain more than 2 maybe's, I'd reconsider and not recruit one at this time. Maybe's, unpredictability, and unforeseeability are key recipes to disaster. So avoid them at all cost.
Until you can answer these questions for yourself with great certainties, it would be unwise to invest your time to recruit, hire, and train a full-time COO for your company. Instead, you might want to consider hiring one on a part-time basis-perhaps some random John Doe or Jane Smith with relevant work experience or a retired executive-to test whether your decision makes the most economical sense.
I have been told that you should never do or go into business with a friend . If it all goes pear shaped 1) you loose a friend 2) it gets really really ugly .
If you wish to have a partner it may be prudent to find a person or persons that add real value and can be a contrast to yourself but you need that person to provide a balance.
Furthermore if you keep friendships out of the equation then you not being swayed by the heart and more from the point of logic and thus your questions resolve themselves