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After losing three early wickets, the 25-year-old helped guide the tourists to 179-4 at the close.
Taylor fell late on for 70, with Nick Compton 63 not out.
"That wasn't ideal, my late wicket, but that happens and we've still got plenty of batting to come, which is really exciting," Taylor told the BBC.
"We're in a nice position. We've got Compo in there who's batting extremely nicely, and we all know how good a nick Ben Stokes is in at the moment, with plenty of batting to come.
"So I think, as a whole, it's been a pretty solid day for ourselves."
Taylor arrived at the crease with England struggling at 49 for three, after captain Alastair Cook fell for a duck, debutant opener Alex Hales made just 10 and Joe Root was trapped lbw for 24.
South Africa paceman Dale Steyn had claimed both openers but steady half-centuries from Taylor and Compton - who both made Test debuts in 2012 before being dropped - drew the sting form the home side's attack.
"We knew what the situation meant and it kind of dictated the way we played," said Taylor, whose partnership with Compton contributed 125 runs for the fourth wicket.
"We kept it really simple and did exactly what we needed to do and focused on our own game rather than the situation as a whole. It was really enjoyable batting with Compo, it was good fun.
"We should be pretty happy with that considering it couldn't have been better bowling conditions for them."
It was Steyn, returning from a spell out with a groin injury, who eventually dismissed Taylor shortly before bad light stopped play.
"It's been frustrating sitting on the sidelines for the last six weeks," said Steyn.
"It was nice to get on the field today. Great to get the first wicket, especially the English captain. It kind of sets the tone for the team.
"We were lucky to get the wicket at the end but we'll take it."
England's batsmen can build on their opening day fightback against South Africa in the first Test, according to James Taylor.