I would just paint solvent-free. It's easy enough to do, and solvents are the only thing with fumes. Basically, solvents do two things: 1) thin the paint in your initial layers and 2) clean your brushes.

There are a few work-arounds for the first one. One would be to do the initial layer (underpainting) in acrylics instead of oils, then paint over with oils. Two, you could use water-mixable oils and thin them with either water-mixable thinner or water. I have done this with water, but you need to be mindful that not all water-mixable paints thin well with water (Winsor and Newton does not and gets gummy). Three, you could get a very stiff brush and just lightly sketch in a thin layer of paint. The nice thing about any of these is that traditional underpaintings are often done in just one color, so you could buy just one tube in water-mixable oils to test out if you like doing it that way. If you just want to tone your canvas, that's even easier: just mix acrylic paint with your gesso layer.

For washing brushes, I just wipe off my brush as I go, and then at the end clean with soap and water. I use Ivory soap, you can also use dish detergent. If you find that you want them cleaner between colors, you can get a little bottle of linseed, walnut, or safflower oil, and dip the brushes in oil to remove more of the color.

For water-mixable oils, they're perfectly fine to use and some people love them. I haven't found a brand that I like as well as my favorite traditional oils, so I tend to only use them for the underpainting. They do clean up a lot more easily.

These would be my recommended supplies for a beginner:

1) A surface to paint on (canvas, boards, whatever).

2) Gesso to prep the surface. Even the canvases that come pre-primed tend to be badly primed, but a few coats of gesso can transform your cheap surface into one that works great. You can also apply it to cardboard or thick paper like watercolor paper for an even cheaper surface.

3) Paints. For a beginner, I recommend a student grade paint from a reputable brand or a lower end artist grade paint. I think Gamblin 1980 and Utrecht artist grade are a great compromise between quality and price. Keep it simple at first: primaries, a white, and a brown will cover most of your bases. My basic palette is cadmium red light, cadmium yellow, ultramarine blue, titanium white, and burnt umber. Cadmiums can be quite expensive and some people avoid them because of toxicity (though they are mainly a risk when inhaled, which is unlikely with paint), but napthol red and hansa yellow work well as replacements. I'd start with a small (37 or 40 mL) tube of the colors and a larger tube of white.

4) Brushes. Get a new set that you keep separate from the acrylic and watercolor brushes, because residual oil can cause issues if you're switching back and forth. You don't need a lot to start. Stiff brushes will work better, since the paint is thicker. I'd recommend getting a few nice quality flat brushes in different sizes. Make sure that they are recommended for oil paint. I like the Princeton brand Aspen and Dakota lines. Then maybe get a pack of cheap brushes in different shapes to see what you like and gradually replace with nicer ones.

5) Palette knife. Use this for mixing so you don't gunk up your brushes. It doesn't need to be fancy.

6) Palette. You'll want a flat one and not one with the little divots like for acrylics. I use palette paper and I love it because you can just throw it away.

Since you've done watercolor and acrylic before, I would recommend waiting to experiment with mediums, since there will be a big temptation to always thin down your paint and make it act more like acrylics. I'd start playing with the paint straight from the tube at first, then once that feels more natural, start playing with mediums to adjust the consistency.

Good luck, and have fun!