Thinking about it, whenever I buy on-line (which is frequently) I usually check out the Terms and Conditions, when I've not used that company previously. Sometimes I go the whole hog and check out their Legal disclaimers too.... it's surprising how often I've been put off by "clauses" which are either nonsensical or else plainly unfair.... and probably wouldn't hold water with Trading Standards, etc.
Next I check to see that they have a contact address and landline telephone number. Lots of companies are very forthcoming and will even state their Company Reg and VAT numbers (depending upon how much I'm planning to spend, I have occasionally checked these out with Companies House on-line - trusting soul, eh
Online security is probably the number one that I would choose from the list - but on the other hand, if I had already used the firm, then "past experience" would have to be considered as joint number one .... ooh-er, split vote here.
Delivery speed and cost are also important, because if the item you are buying is a must-have bargain, there is no point in buying it on-line if the p&p is going to be very high.
Good customer service is a very big influence. I am more likely to shop at the same online store again, when experiences have been favourable
So - I shall vote Online Security, which is something we all need to consider when handing out personal details, etc., but with the above-mentioned reservations
.....sorry to be difficult