The problem I have with going with a used bicycle is that I've seen the used bicycles that show up in the local "thrift" shops here ...... and they are in SCARY shape!!
Most of them have cables that have long since rusted away and died; often the previous owner didn't realize that the left pedal has left-hand thread and tried to force it on or off, thus stripping the thread; gears have only half their teeth; some of the ones I've seen are completely missing their chains; wheels are bent and badly out of true; the tires have rotted away; the frames have nicks, dents, scrapes etc.
And often these bicycles were originally purchased from a local department store anyway!! Only now they are in really, really rough shape.
The reason these bicycles are in the "thrift" shop is because they are in such bad shape that the previous owner realized he'd have spend a fortune to fix it all (more than he spent on the bicycle in the first place) ... so it was just easier to give it away ... and the personnel in these "thrift" shops haven't the faintest clue that the bicycle is supposed to have cables and a chain, etc., so they just accept it, slap a $25 tag on it, and hope that someone will buy it.
At least with a new bicycle (even if it is from a place like Walmart) the cables are new, the gears have all their teeth, there is a chain, etc. No, a Walmart bicycle is not in the same league as a much higher-end bicycle from a bicycle shop, but IMO it can be a better choice than a used bicycle for someone who doesn't have a lot of money, and who doesn't have a lot of mechanical knowledge, or time, to fix a used bicycle up into a rideable condition.
IF a person could find a good quality used bicycle in good shape for an inexpensive price, then I might say to go the used route. And for that, I'd check the "Buy and Sell" section of my local cycling association's webpage.