As Rebekah points out, we can't give you specific advice, much less numbers, without knowing the situation (and providing you with a Consumer Notice). Won't stop me from spouting generalities, though :-)
Do you have a Buyer Agency Agreement with "your" agent? If not, the agent may be working under subagency, which means they represent the seller and *only* the seller. If you do have a buyer agency agreement, your agent is a dual agent -- working for both. That means the agent can't do anything that harms either party, and is bound by confidentiality (e.g., she can't tell the seller your best price if she knows it). Under sub-agency, there is no confidentiality -- anything you say can go straight to the seller (and be used against you in the negotiation).
With REOs you typically have a pile of addenda that say the property is "as-is," they won't turn utilities on, etc. They also put extra conditions on the sale, such as requiring the buyer to pay all transfer taxes. You generally can't ask for seller assist on these deals. Even if it isn't explicitly prevented by the addenda, it reduces your offer by 3% in the eyes of the seller. You will probably be the only buyer asking for closing cost assistance.
If you do have a Buyer Agency Agreement, the agent should be helping you (e.g., with a BPO). If he isn't, go to the broker, who should either light a fire under him or assign you a new agent. If you don't have an agent ("your" agent is a sub of the seller), *get one fast*, before the bank takes one of the other offers.
Your "highest and best" depends on your personal financial situation and future plans for the property. Only you can determine that figure; an agent can then help you determine whether this particular property is worth it.