Koshkin

Agree, Rudin is excellent as a second course on real analysis, but as a first one it is absolutely terrible.

Also, his Advanced Engineering Mathematics.

Calculus by M.Kline would be not a bad start.

There's also the Demystified series, which is good but has fewer exercises.

For a broad (yet detailed) overview, Mathematics by Aleksandrov et al. is exceptional.

The Schaum's Outline Series.