The first thing to consider is - is the phone actually the brand it purports to be? We are all familiar with the general appearance of the major brands of smartphone but check the description to make sure the seller describes it as that particular brand of phone. If it has very few bids up to a fraction of the price you normally expect to pay for that brand of phone, it's a sign that something is not right.
FEEDBACK is vitally important; the seller may have 100+ plus positive feedback but check it carefully to make sure that is RECENT i.e. the seller didn't suddenly stop selling things a year ago and has now started selling again! Also check for "negative positives" such as very slow delivery.
Lastly, the IMEI number is a 15 digit "registration number" and each mobile phone has it's own unique number. The IMEI number should be printed on a sticker on the box, together with the "S/N Number" - the Serial Number for the phone. If you buy a phone not in it's original box, obviously these stickers will not be present. However the IMEI and S/N numbers should also be on a sticker underneath the battery - if this is not present you should be worried. The IMEI number can also be found in "Settings>About Device>Status" and should match the number on the box and sticker.
You can check your phone's status by entering the IMEI number in a box on the website which can be found by searching for "International Numbering Plans IMEI" which will tell you what make of phone it is and whether it is blocked or deactivated etc. This should be done as soon as possible after you receive it so that you can resolve any problems within the ebay 45 day resolution period.
In conclusion, enjoy your new phone!