When you receive an offer on your property, the main two things to remember are:

1. Now is the time for negotiations and stipulations, not later. You may want to make this clear to the potential tenants as well.
2. It's
   your property. Letting agents work on commission so they want you to
   accept the offer. If there is something you are not comfortable with,
   try and solve the problem but if all else fails, don't be afraid to
   reject the offer.

Having said that, you need your property to
be occupied so don't frighten the potential tenants away by asking for
too much. Where there are parts of an offer you are not comfortable
with, problem solve - this is what lettings negotiators do. For
example, ask for a larger deposit if they have a pet or offer a break
clause if the tenants want the security of knowing they can move out of
the property if they don't like living there. Tenants can often seem
demanding and awkward but remember that landlords and letting agents
don't have the best reputations and many tenants have had a deposit
witheld unreasonably.