Packing is important - you want your art to arrive with good protection and care. 

Price is important - you don't want to overpay.

Service is important - you want to be treated like a customer, not an inconvenience.

But the most important part of any art purchase is to know that it is authentic and genuine. 

Forgery is as old as art itself, and wherever there is money to be made, criminals will not be too far away.

Gladly, there are several ways of eliminating a non-authentic piece. Most are in the pre-buy. Dealing with a well reputed dealer, gallery or auction house is a good start.
Buying from the artist directly is as good as it gets, or their primary gallery.
If you are buying from the secondary market, you need to know the provenance, where the original purchase was made, and paperwork or certificates to support it. 
Once the item is in hand, you can check the paper is as described, the size is correct, the blind stamp looks authentic, and the signature has no dependencies.  
On a fake print, something will jump out as suspect.
We may contact the printer, the gallery or even the artist. Wasn't this print supposed to have deckled edges? Didn't the artist sign in pencil and always on the left hand side for example. 

Spotting the fake in hand isn't as hard as you would expect, but unfortunately  this can be too late.
At Eben Contemporary we pride ourselves on making sure we have done our due diligence in checking provenance and the work itself.   
Most are from the primary source, and any non-primary source items are scrutinised.
Our best advice is: if in doubt, walk away, we do. 

Condition, on the other hand is different. A piece can be authentic but in poor condition. We deal with a lot of edition prints. Nearly all prints are printed on paper, and that can be problematic.  
Poor storage, framing, ultra violet damage, we have seen it all. The important thing is that the condition report is accurate. 
Our policy is to make any issue prominent rather than understate it.

In the words of Radiohead, we want no alarms and no surprises please.