Every handgun I own I bought online, and have had no problems--quite opposite, it's been a good experience in all cases. Dealers at gunbroker are rated by the 1,000s of people who actually buy from them, and you can easily see how many transactions they've had at gunbroker. Given your plan is to buy a new gun rather than a used one, that certainly removes the 'sight unseen' concerns I'd expect.
I think it's significantly easier to get a good idea of the credibility and reputation of an online dealer than it is to buy any other way, although if there's some problem you feel you need to get handled by the outfit you purchased from, it could certainly be far more difficult than going back to the LGS you purchased from. I don't worry those issues as, if I had a problem with a firearm, the dealer is probably the last place I'd go to get it fixed, whether online or downtown.
My experience has been excellent. I've purchased 6 new and 4 used online.
All weapons were received at my Club for transfer within about 2 weeks or so, some much less. All used guns, without exception, were in better condition than described.
There is no way I know of that I can quickly and easily find out what the overall relative satisfaction is of the last 3,500 people who bought guns from my local dealer. I can do that in 20 minutes for a dozen dealers online--less time than it takes me to drive to my LGS and without having to deal with them and other clueless customers waving the guns around.
For a 'commodity' 9mm auto, I wouldn't even consider buying any other way. Read the terms and conditions (which are published for you to read, unlike at the LGS generally), and if the language is poor, not to your liking or sounds like the dealer generally doesn't really like customers, move on--there are dozens more to choose from at the click of the mouse. I personally wouldn't likely buy from an online dealer that only did business through their own storefront--but rather would prefer to select a source doing business under the somewhat protective umbrella of a brokerage such as gunbroker.com or gunsamerica.com. I feel in most cases such brokerages provide some air support in terms of arbitration, etc., should a deal go tango--same as with eBay and Amazon.