Obviously, the price is usually the most important element, but there are other factors that make an offer more - or less - attractive. For instance, one obstacle is a "contingency," a clause that allows a buyer to back out if certain conditions are not met. Of course, offers with the fewest contingencies are most attractive to sellers.
When it comes to contingencies, first-time buyers are often better prospects for a seller's home than move-up buyers. Why?
Because offers from homeowners usually are contingent upon the sale of their present home. Even if a move-up buyer has an offer for their home in hand, their buyer's offer may be contingent on another contingency (or sale) - and so on down the line. If one transaction in the chain falls through, they all might.
Cash offers can also be more attractive to sellers. Why?
After all, the seller will get their money at closing whether or not the buyer has cash or takes out a loan. True, but cash offers do not require lender approval, and loan approval is never a certainty - it may delay closing. (incidentally, for this reason, buyers who get pre-approved for a loan have an edge over other buyers. A pre-approved buyer is the same as a cash buyer.)
Buyers offering a larger-than-customary amount of "earnest money" (a deposit that accompanies an offer) can be more appealing, too. More money demonstrates greater sincerity and motivation to close the transaction.
Naturally, sellers are always looking for the best price for their home, but remember they also want an easy, trouble-free reliable transaction. Thus, as a rule, the fewer the contingencies, and the greater the commitment - the smoother the transaction.