A couple things I would add
1. AFAIK, the shifters all adjust tension with just a screw. All the ones I've had have a d-ring or such that you can adjust by hand. But if there hasn't been a lot of maintenance, they may be kind of frozen, and you don't want to overdo the force and break off the d-ring. My preference was to tighten the shifter just enough that it wouldn't move on its own and no more, so it was easy to push/pull.

2. As far as shifting, I would say typically when you shift the back from a bigger to smaller cog as you move the shifter the chain falls onto the smaller gear and you are good to go. But shifting to a bigger cog you may need to slightly "over shift" to get the chain to "jump up" and and then ease off until it is nice and silent. Note that there is no need to go "one at a time", but smoothness counts.

As other posters already advised it is typical to have to adjust the front derailleur position a little to stop any rubbing.

3. Unlike indexed shifters, there isn't any thing to prevent over-shifting except the limit screws on the derailleurs so make sure you have these set correctly.

So as you get experience, it is OK to move the lever a bit slowly and get a feel for things. Over time you will be able to accurately and quickly shift up/down one two or three cogs with minimal adjusting.

scott s.
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