I use 10mil (0.25mm) traces as default together with 28mil (0.7mm) diameter and 12mil (0.3mm) drilling vias. I would somehow consider the 28/12mil via the industry standard. Every PCB shop can make it. I reduce dimensions with decrements of 2mils when I really need to. I always try to stay above the PCB house minimal requirements (not always possible due to tiny packages). Additionally, I keep 10- or (and) 5mil grid for components placement and routing. I typically avoid setting the grid resolution smaller than the minimum pitch of the smallest component on the board.
For slightly higher-density boards, you can refer to
http://www.ti.com/lit/ug/tidudo9/tidudo9.pdfchapter 4.3. There I go down to 6mils with a four-layer board and the single side components placement.
I hope this helps.
edit: To answer the second part of the question - I am generally uncomfortable with the drilling below 0.2mm. (8mil), annual ring below 6mil and trace below 6mil. This gives the size of 20/8mil for my smallest vias.
Keep in mind that these are my personalized go-to settings when I do my projects and let them manufacture at shops like OSH park, Betalayout, SeedStudio etc.
You can go for smaller sizes but you typically need to pay extra for smaller drilling etc.
Also, this applies only to 1oz or 0.5oz copper plating. You may need to talk to the PCB house if you want a design with a thicker copper plating. Check design requirements from Betalayout. The webpage is helpful.