Disclaimer: I haven't taught the kind of course you describe, so please take my recommendations below with a grain of salt. Nevertheless, I hope they're helpful.
John M. Lee's Introduction to Topological Manifolds is a great place to start for the basics of topology, topological manifolds, the fundamental group, covering spaces and just a touch of homology. It's written at an introductory graduate level and the author has taken pains to write clearly and in detail. For smooth manifolds, you can follow up with his Introduction to Smooth Manifolds. However, if the latter book is too long and detailed for your course, you could switch to Loring W. Tu's An Introduction to Manifolds, which is also well written.
If your students have already had some general topology, you could either skip or go lightly through the early chapters of Introduction to Topological Manifolds, giving you more time for smooth manifolds later.
A book that I'm less familiar with, but looks promising, is the recent A Short Course in Differential Topology by Bjørn I. Dundas. It introduces smooth manifolds, the tangent space, regular values, vector bundles, flows and a few other topics, with the assumed background on general topology given in an appendix. Admittedly, it doesn't treat several of the topics in your list, but you said you're less worried about the specific topics. The author has a PDF version available at https://folk.uib.no/nmabd/dt/dtcurrent.pdf. The PDF isn't identical to the published version but it's close enough to give you a good impression. Note that despite the term "differential topology" in the title, it covers much of the smooth manifolds basics you'd find in the early chapters of many books of manifolds, be they heading toward analysis on manifolds, differential geometry or differential topology.