I recomend the book "A world Af difference" by Harry Turtledove. In this novel Mars is habitable and in fact habited. The first probe that is sent to Mars (Minerva as it is called in the book) sends a picture of a creature welding a stick back to Earth, shortly before the earth loses signal. So the USA and the USSR decide to sent manned missions to that planet...
Sounds like a first-contact type story. I'm more interested in the economic/political and technical development of the world's space programs in a Solar System including a habitable Mars and Venus (which I think would provide enough additional impetus to space exploration just by being habitable, without any need for intelligent life). The habitability of Mars and Venus could be discovered without probes: The presence of significant amounts of oxygen in the atmosphere could be detected from Earth, and oxygen requires the presence of plant life.
I'm interested in questions like the following:
Would the pre-Moon US spaceflight program have received additional funding and developed differently, or would the point of divergence have come after Apollo (with the Apollo program being extended to include the extra missions that were never flown in our timeline, etc)?
How would the Soviet program have changed (would the N1 project have fared better with more and/or earlier funding, would the Soviets have scrapped it and moved on to something else, or would they still have given up)?
Who else would have made moonshots in hopes of moving on to Mars and Venus?
What would the evolution of launch infrastructure have looked like? Would the US, moving on from Apollo, have used a derivative of the Saturn V designed for mass production or something entirely different? Would the Saturn V even have been developed in the first place?
What would the interplanetary transport infrastructure look like?
Etc.
Mars problem is its atmosphere.
Mars' problem is a bit bigger than that. First of all, it's gravity well isn't deep enough to hold a significant atmosphere, secondly, it's far enough away from the Sun that it would be difficult, if not impossible, to get it to stay warm enough to be habitable, no matter how you tweaked it.
In my musings on the issue, I've been assuming that Mars has a very large iron core such that it is twice as dense as the real Mars with the same radius (thus, twice the mass). This gives it just enough gravity to hold on to a significant atmosphere in the long term. The temperature issue I'm solving by assuming a relatively high (but still breathable) CO2 fraction in the atmosphere, combined with a fairly dark surface (though liquid water implies that there will be significant polar caps, 'cause the temperatures still won't be balmy, and the reflectivity of the polar caps may just cause a runaway icehouse effect across the entire planet).
And Venus is to hot with a dense crushing atmosphere.
It's rotation rate is also probably too slow, at least for how close in it is. Venus is actually to some degree easier to make habitable (in terms of presuming different characteristics for the planet in a fictional scenario, not in terms of actual terraforming) than Mars, despite its more extreme real-life surface conditions. "All" you need to do is assume an Earthlike atmosphere and rotation rate, and that the high temperatures cause enough evaporation to form a planet-wide cloud deck much like Venus actually has (except with water instead of sulfuric acid in the clouds). If you don't get a planet-wide cloud deck, then a lot of light gets absorbed by the ocean instead of reflected by the clouds, and the temperatures get too hot for humans (and probably for any life). If you do get a cloud deck, the clouds reflect enough light that temperatures, at least towards the poles, can be survivable for humans. The real-life Venus, for example, has habitable temperatures around the cloud deck, but the atmosphere isn't breathable, and it's thick enough that adiabatic heating between the level of the cloud deck and the ground makes the surface temperatures incredibly hot.
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In this scenario Venus may still be swathed in cloud,
Insolation at Venus is high enough that it could not be habitable without being swathed in cloud. Fortunately, I think you'll get enough evaporation from an ocean that that would be the case.
but Mars would likely be more observable (and could also garner more interest, especially with more obvious features of habitability).
Making surveys to allow a safe landing would also be easier, though my bet is on water landings near coastlines, which could be surveyed for with radar.
Rather than images of a barren lunar landscape, images of familiar landforms like bodies of water, rivers, and mountain ranges could spur further public interest in the planets.
Post-Apollo (or post-N1/L3, this is alternate history after all, though one could argue that the US was more likely to see success in any case), enthusiasm and funding probably wouldn't drop like they did in reality. The case after Apollo was to press on to Mars in any case (though Venus may be a better goal owing to its proximity), and the purpose of STS was to build the infrastructure in space that was to make this possible.
Undoubtedly STS would have hit the same technical hurdles that caused its unsuccess in our history, though things may differ owing to differing priorities and amounts of funding.
My hope is that the heavy beyond-LEO focus would cause STS to be ruled out, though in working out a fictional scenario, it could be used to add drama (the US makes the first moon landing while N1 languishes, but the USSR makes the first Mars/Venus landing because difficulties with STS slow the US down).
Apollo hardware might be repurposed; a relatively simple set of alterations could have been used for a manned Venus flyby in our time, and such a mission plan may well be the first human mission to the planet in such a scenario.
It should be noted though that there is much uncertainty over interplanetary flight today, and that the maturity of long-term spaceflight science was considerably less complete in the 1970s. It would have been a dangerous mission.
Apollo (or N1/L3) hardware could be adapted to a planetary mission, though various new hardware would also have to be built (how do you land on Mars or Venus? How do you take off from either of them, especially Venus, with its near-Earthlike gravity well?).
For landings, my bet would be a capsule for dropping crew, and the offspring of the space shuttle and a flying boat for heavy equipment (unlike the Shuttle, this would be designed as a one-use deal, and I'm heavily leaning towards launching the components individually and assembling the thing in Earth orbit, because of the shortcomings of STS).
For takeoffs, especially from Venus, I imagine you'd have to have at least some sort of an established surface base, and that you'd have to field-assemble an Atlas/Titan type vehicle (whose components would be delivered in heavy equipment boats).
The first people to land would probably have to wait several years to leave, and there would be a greatly increased stranding hazard. On the other hand, being stranded would be much less of an issue than it would be on an uninhabitable body.
My bet is that the Moon would be left largely ignored (relative to Mars and Venus, not necessarily relative to the interest given to it in our timeline), though it may capitalise on increased funding and R&D work for the planetary programs. It just isn't as interesting, and the next goal ahead is far more important.
Of course, it gets tougher to speculate the further you go from the 'point of divergence'. One may well speculate- entirely within the bounds of what could be agreed on as plausible- quite wacky scenarios involving grand spaceships and great exoatmospheric epics (or on the slightly more humorous side of the scale, an epic battle between the US and USSR to wind the hearts and minds of the Martian populace).
I think that even by 2012 settlements on Mars and Venus would largely be scientific in nature, and you probably wouldn't have more than a few hundred people on either planet, so I think all of the Cold War saber-rattling would still be going on on Earth (and maybe LEO).