I read several blogs and interview of several Angel investors. My understanding is they are mostly asking for Preferred Stocks.
What are most common terms and conditions they lay down in Preferred stocks?
The whole point of having Preferred stocks is to have special treatment relative to other stockholders. You can sum up the benefits typically requested in two main areas: payment and governance.
Payment: in a (bankruptcy or) sale of the company, stockholders split all the money left relative to their shareholding, after debts are paid. Preferred stockholders may insist on being paid first. For instance, it is a common term to say 'if we invest $1M, we must be paid $1M or $2M back before anyone else gets paid anything'.
(Similarly, when dividends are paid, preferred stockholders may insist that they get paid dividends before common stockholders and/or they get guaranteed annual dividends when common gets nothing. This is less usual to see in VC.)
Governance: typically, a majority of the (common) shares of the company is needed to enforce key ownership decisions, e.g., whether to sell the company, change the board or management, and so on. Preferred shareholders may insist on certain governance provisions, whereby you need a majority of the preferred shares (possibly but not necessarily as well as a majority of the common shares) in order to take key actions like those listed. They will typically name the exact actions, and typically it is around sale of the company, taking on debt, transactions with owners and the dreaded board and management changes.