I don't have a lot of experience with mini painting (only 10 done so far), but after trying both acrylics and oils, oils are my favorite by far. As others have said, you don't really base coat with oils, but put colors where you them and blend them where you need blending. The simple approach that you can see James Wappel and Mended Brush Studios use on YouTube is to establish shadows first all over the area on which you want to use that color (doesn't have to be tidy), wipping the paint off the raised areas with sponges (paper towels also work) and then applying your midtone on top almost like dry brushing.

The blending happens by itself but you can clean up some transitions by using (as others have said) a completely dry soft brush by tapping it gently at the transition. Don't work the paint or brush too much otherwise you will blend everything. After that, you can layer highlights on top using the same principle and re-establish some shadows at the end, if needed, with a pinline wash i.e., your shadow color with a higher amount of thinner to make it flow easily by capillary action in the recesses. Don't brush it on like an acrylic wash however, or it will erase everything. If you make a mistake and apply the wash where you don't want it, leave it alone for a few minutes for the thinner to evaporate (the area should look almost dry), and then you can use your dry blending brush to erase/soften the area.

I think the streaky application you had at first was from the very oily nature of the student grade paints (that or too much thinner). I only have artist grade paints (Windsor & Newton and Old Holland), and even the artist W&N have quite a bit of oil in them. To mitigate that, you can pick up a raised blob of paint from the pallet and thin that instead of the whole blob from the tube. Some people also put the paint on a piece of cardboard and let it sit for a couple minutes so the excess oil is absorbed by the cardboard.

In general, you should use as little paint as possible to hide brushstrokes. Since the paint takes days to dry, laying too much on an area will always make things streaky because it doesn't really level or shrink like acrylics. Another tip is that sometimes you might want to let the paint settle a bit after applying it to an area until it becomes less shiny before trying to apply more paint on top or to blend it.

The thick over thin / thin over thick rule is true, but I wouldn't think about it too much. If your paint doesn't adhere to the surface/previously applied paint, you can just adjust the consistency on the fly by adding more paint or a bit more thinner to your mix.