- Counteroffer. Seriously.
- If you're profitable and can keep on going, make this -very- transparent to the people approaching you.
- "No deal is better than a bad deal" is very true. Make sure the deal makes you happy.
- Having an experienced negotiator along is going to make this a lot less nerve-wrecking. Try finding one, somehow.
The vesting over 4 years is long by industry standards; understandable though if the buyer really wants to keep the founders on board. If you lose key people after acquisition, you might as well not have bought the company. I suspect the buyer got burnt on this in the past, and now compensates with very long vesting periods.
Creating an impression that "the first offer is the final offer" can safely be assumed to be negotiation tactics. This is what they are paid for; the people you're talking to do this sort of negotiation all the time. You are fencing with someone that has practiced this for years, and they have much less to lose than you. Do not assume malice, just assume that their job is to get a good deal for their employer.
Be frank: Tell them what you think the value of the company actually is. An M&A deal is like getting married: If you don't feel that it's the happiest day of your life when you sign your company over, you probably shouldn't do it. A little bit of cold feet is to be expected, but generally you should -not- enter a deal where you have a bitter taste in your mouth. That would do neither you (nor the potential buyer) any good.
Get yourself advisors (experienced ones, preferably); but be careful: Keep their incentive structure in mind. Some have a lot less to lose than you (e.g. if the deal breaks apart, they lose a couple of hours of work), but can often gain much more from risk-taking (as they usually want a percentage of the proceeds).
Your impression that a lot of advisors seem like they have something to sell to you is correct, because they do. Finding one that you deem trustworthy is important; personal connections are usually more helpful than shopping around.
It is not unheard of to not get the LOI before the basic terms are agreed upon. The buyer wants to avoid giving you something in writing that you could use to shop around.
I was in a very similar situation to you recently. Is there any way we can have a chat ?