Its a matter of knowing which tech becomes viable and to what degree first. I want to emphasize, it really can be done now, but I wouldn't do it the way they are, and I wouldn't do it now anyway because I expect newer tech to make itself available and be a game changer. If I had to do it today, because someone told me, 'now or never', then I'd be doing the following logical assumption:

1) There is reason to believe technology will not make this easier on any time scale of relevance
2) Get some of the eggs out of the basket

That would lead me to wanting two or more mostly self-sufficient bases. And that means In-Situ Resource Utilization (ISRU), which is always my leaning anyway. I don't go for exploring, I go for mass exploitation. I won't even discuss space elevators or cheaper propulsion (fusion) because those are total gamechangers, you get either even vaguely practical and we stop talking about sending a few people or a few dozen with concerns over weight, we start sending flotillas. Ten years after you get a fusion drive compact enough to provide meaningful thrust or space elevator material where a yard of the stuff of the right width doesn't cost more than most people earn in a year and we'll be firing ships off regularly to several places. If you've got both then we'll likely see genuine commercial ventures. So discussing those in the mix is sort of redundant. Assume nothing new.

1) Get a real orbital habitat up there. I'm talking about things of the Ark I class, smaller probably, but in the zone of size where hydroponic food growth and actual assembly labor is doable, and a rotating section can provide at least some gravity.

2) Get another up there at the Lagrange point between Earth and the moon.
2b) Probably place it a bit closer to earth with a Kevlar, or an in-situ Quartz whisker maybe, space tether hugging it to the moon instead. Pearson did a good write up on this for NASA some years back, and I'd argue if you can't spin a tether in-situ that cislunar station is probably pointless.

3) Moon base - Probably at the Shackleton Crater, probably a few of these, where you find yourself a decent small pit, or dig one (digging on the moon is very easy, and nothing that doesn't need sunlight should ever be above ground). You get that full running first. I'd have them carve out a couple cylindrical pits we could stick rotating sections in, floor sloped to combine lunar gravity and centrifugal force for something closer to Earth's. Essentially an underground donut spinning in the vacuum in which they emerged for necessary work. I would keep expanding the thing until could provide air, water, power, and food for at least fifty people.

4) Learn fuel refining - We'd then start extracting fuel on the moon, aiming for at least five tons a day, and expand the base until it was achieving at least that of surplus a day. When that was achieved or safely in sight, step five.

5) Begin constructing Martian colonial vessel. I would budget no less than 20 tons per person of payload and assume 200 tons of fuel per person. I'll just assume this takes five years and we have something like 6000 tons of fuel available for the ship itself, or 30 people. During this I'd be trying to get multiple minor and different pre-arrival stuff in place. Fuel pods in LMO, ground supplies, robot constructors, etc, always try out different things and the moon base would give some insights.

6) Launch, I'd send my 30-man ~600 ton ship to Mars. Since the moon is still pumping out fuel I'd be sending more of it, or more supplies, or fueling a second ship of equal or smaller size.

That's about it, I'd be focusing far more on that Moon base because if the shit hits the fan they could retreat to underground bunkers with supplies until we could bring in repair equipment or bring them home. I'd be aiming to get that Mars colony up to 200 people, but what I'd really want is to get that moon colony to such a huge size that it could manufacture everything we needed except some of the more sophisticated equipment. If at any point we got to the point that all we needed from Earth was a person and about their own weight in sophisticated tech, I'd start sending ships of a couple hundred people off to every decent looking asteroid to clone the moon base, not the mars base. Mars is not really that handy, it is not 'easier to live on' then an asteroid, not much anyway, and I'd be wanting to spill our eggs all over the system in groups of 100-200. At asteroid, dig in, carve ever wider cylindrical bits, stick something rotating inside to live and mostly work in.

The problem here is that there's never going to be a solar economy the way people envision it, partially because while Earth is a wonderful place to live it is also just about the suckiest place to do space travel from. Massive gravity well and a thick ass atmosphere. On an asteroid you can coat the place in solar panels and jury-rig a railgun to fire ships to neighbors without even needing any more fuel then is necessary for minor course corrections, you can even land that way. So a few dozen asteroids in reasonably near proximity can each mostly self-sustain but run a small specialized industry for trade to its various neighbors. Asteroids in the belts of any meaningful size (bigger than a kilometer across) number about a million at least and while the belt is in truth incredibly empty the energy needed to travel between asteroids is tiny. You might need to travel a million miles to get to one but you could still shoot it with a rifle.

No such luck here. We've also got the issue that the only thing these places have that we don't have more and cheaper here is the item called 'not here', in case bad shit happens here. In reality bad shit is likely to leave more people here then they would have anyway, with more resources too. Short of Grey Goo it hard to imagine a catastrophe on the planet that we couldn't rebuild from more easily here then they could from there. There's a lot of silly advantages people have sort of conjured that we call advantages only in the context of in-situ, not for the ends they think:

Minerals: Nonsense, mining asteroid or other worlds for crap to be brought back to Earth is absurd. Earth has roughly as much of this stuff as all of them combined. We talk about exhausting minerals but what we mean is exhausting cheap ones, and mostly in the context of expanding need. A stable population can mine its garbage heaps for almost everything it needs much cheaper then off world importation, and anything that makes the latter cheaper makes the former cheaper. Space Elevator? Sure, the reverse is a mine lined with the same stuff. If you can build a super-strong cable tens of thousands of miles long you can build a shaft tens of miles deep, and you can also drill thin shafts faster and cheaper to explore for good pockets, if you've got yourself graphene sleeves to line the route and sharper then diamond drill bits.

Hydrogen for fusion: Again, we've got more than they, except the gas giants, and more then we'd ever need. If you get to the point you need off world hydrogen then you're at a point where you've got heat issues, and are thinking about removing your own atmosphere and configure the surface to be one giant heat sink configured to radiation of infrared. You'd be bringing in hydrogen only in the small quantities left over for ships returning from dumping of people/goods because it just isn't something you need much of.

Food: It is infinitely easier to build even vertical or subterranean hydroponic facilities powered on-world fusion or near orbit solar powersats then to grow food there and shuttle it down. If yo haven't got fusion or space elevators then you have to grow all your food on world anyway, and if you do you don't need to bring it in.

Hence: Eggs/basket - we expand offworld just to minimize extinction options. If those are actually capable of being self-supporting then they'd likely provide all the resources and people needed for further expansion, not Earth.

Now, if you're asking my opinion of what will happen, then I'd say in around a century we'll just launch robot factories to places to set the entire show up, or mostly so, and send in people when the light lag makes having them there more convenient. I would bet on colonizing all those million 1-km+ asteroids in the belt with a few hundred or thousand people first before we get around to trying to colonize Venus or do anything inter-stellar. I'd personally bet on having several million off-world habitats before we even have anything at another star, let alone people.