As a part of my job I do some background checking on various businesses, often internet-based. So, depending on the amount of money you plan to spend and the amount of time you are to devote, here's some helpful suggestions once you have a specific internet coin dealer in mind.
Make sure to take good notes during the process as you will need to refer back to them throughout. Note also this is not in order and you might jump around and repeat certain steps quite a bit depending on the information found in a later step.
-first look at their website. cruise through it, get an impression. Make note of spelling, punctuation, item descriptions, etc. View their terms and conditions, what do you think? Things like no returns for any reason ever, this is a definite negative. Hit their "about us" page. Does the site match what they say they are? IE if it's touted to be a super big consortium and high-tech organization the site shouldn't look homemade nor should it have a bunch of typos. If it is a sole proprietorship, you can be a more forgiving.
-put something in your cart & proceed to checkout. When it comes time to enter your information and payment info, is it a secure page? If no run away!
-are they an actual store, or web only? If they say they are an actual store, you can do a google street view of their location and make sure it really is an actual store, not a mailboxes etc. Nothing wrong with a mailbox etc location specifically, as long as they don't bill themselves as an actual store. And make sure any photos of their storefront which may be listed on their site match up to what you see in the streetview.
-is there a phone # listed anywhere? If not that's somewhat of a red flag, you want to have a phone # listed in case there's problems. If there is one call it, both to make sure it's valid and to ask a couple of questions-- questions you'd expect someone knowledgeable in this field to know offhand.
-do a reverse lookup on whitepages.com for the various phone numbers, fax #'s etc. A business phone or fax is nearly always listed-- esp for a brick & mortar store. If not that's possibly an issue. If it is, does it match the address for the store?
-do they do
ebay? Look up a few of their auctions. How are they described, are they overhyped or misleading? Look through their feedback. More specifically look at the feedback as a seller section. Don't just look at positive/negative or the percentage, this means nearly nothing. Look at their feedback and scan through the actual texts. Pay special attention to ones that mention the actual item, and look for "positive" feedback that is either ambiguous or negative listed as a positive.
-look them up on the BBB website. What's their rating there, are they a member? Does their time in business match with the stated time (if any) on their website? Any complaints? How were they resolved? How many complaints are there versus the indicated size of their business?
-does their website list any affiliations or are they a member of any organizations? If so go to that organization's website and see about verifying their membership. I'd expect that some may have listings of any complaints lodged against their members (I don't know that for a fact, I've never dug that deep on a coin dealer, but many trade organizations do keep lists of such things)
-go to whois.net, you can look up the registration on their domain listing. Listings made by proxy are becoming more common, but I'm always somewhat wary of them.
-certain counties or municipalities have online lookups for business licenses, look it up. Make sure they have a license and that it matches their business or a related business. For instance it wouldn't surprise me to see a coin dealer with a license as a pawn broker, though it would make me slightly more hesitant. But if there was a license as a plumber, I'd begin to wonder what was up. (this one is not definitive--- lack of a license is often because the website you're looking up in is impossible to use or has some weird restrictions---- but if they do have the proper license and it is not expired it is a checkmark in the positive column)
-If you've found any other websites so far, go check them out. -google their website name(s), company name(s), alternate company names, address(es), email address(es), phone numbers, fax numbers, owner/president name, and anything else you can think of.
-Look for other aliases... more company names, etc.
-Look for complaints but remember that a certain amount of disgruntled customers are going to pop up-- that's just the nature of things. BUT when it's a pattern, across different websites, different dates, with different writing styles, that's a possible problem.
Last, take all of the above and make sure it all matches up. You may notice inconsistencies, a few are to be expected--- but lots of them, or big ones that just smack of something wrong, and you might need to keep looking.
That's the basics on researching... after that I'd probably place one or two smaller orders, make sure you're happy with everything-- quality, customer service, etc. Maybe even return one or at least call and inquire about returning it and see what kind of a reaction you get.
I know this is a lot, and maybe it's overkill. In fact I'm sure it is. But I got on a roll, and it's all typed up, so here it is.