Literally, every offer from WTSO includes free shipping with a set number of bottles-rarely more than four, sometimes as low as one. The number goes up (generally) as the price goes down. LastBottle does the same. FirstBottle has a similar policy–generally either a dollar amount or a number of bottles. They bought Invino a while back, and the policy there is free shipping with six bottles or $150 (I think) spent. WineAccess has free shipping with six bottles or $120 spent (and increases the discount on the wine as the number ordered goes towards a solid case). Garagiste used to be unpredictable and a bit expensive on shipping, but is now about $2.50 per bottle; that is offset by not adding sales tax. (Not sure if they pay it from the list price, or if they can claim no brick/mortar presence and not collect it). I can probably tell you a few others, but I do pickup at JJBuckley and occasionally RWCo, since I live nearby their warehouses, so I haven’t got those memorized, and anything else like WineX, LAWC, etc would be before the pandemic, I think. The Wine.com option for shipping is like Amazon Prime, but Wine.com has noncompetitive prices to begin with, and who wants to pay up front for shipping?
See, I do have experience in “this market segment,” as well as in purchasing from retailers, wineries, and (once in a while) supermarkets and big box stores. (I wrote a big piece for another site, now defunct, on the online market, years ago.) Not sure who stole my trust fund, but I must have had one, I guess. Meanwhile, maybe look at how the internet has changed rackjobbing, and take a look at what happens when a new vintage shows up on the shelves and the distributor still has some of the old one in the warehouse.
Now, for the OP: Everything Greg Tatar says about wine is the gospel truth, until you start a blind tasting. [I am not being sarcastic–he’s an encyclopedia that just happens to be 6’5" tall or so.] And all of the sites have to be double checked because the “comparable” or “best web” prices are arrant nonsense (kind of like the quoted post above), and the hype about the wine is, well, hype. I wouldn’t start my wine journey on the flash sites, but I find some things with limited distribution through WTSO and LastBottle (esp reasonably priced Italian wines from the Langhe and Montalcino) on those sites; I see what critics I like said about them, or if friends posted notes on CT (sometimes the critic and the friend are the same person), and I’ve discovered some reliable faves that way–Cascina Luisin, Rivetto, Ghisolfi in the Langhe; Caparzo, Molino del Piano, Vitanza in Brunello, to name just a few. Buy locally to start unless your local wine sources are really bad, then keep buying locally and add in the flash and other sites as you start to know what you like and see them listed. Get into this hobby and you can keep a few businesses in the black before you know it.