I'm going to disagree slightly that a starting set of oils are $100.
Here is an introductory set of Gamblin for $69. And THIS ONE is only $41. Gamblin is a very solid mid-range artist quality brand. Avoid student grade like Winton or Gamblin 1980.
You don't need the large tubes yet, even in white, unless you plan on doing very heavy impasto (thick strokes) or extra large paintings. If you burn through a color and want to keep going, then you can upgrade to the larger size, but overall you're going to use way less paint than you expect once you start mixing in mediums and solvents.
In addition to the paint, here's a few more specific suggestions
Gamsol This is the most refined odorless mineral spirit. Again, a smaller bottle will get you started. You save a bit of money in larger quantities, but what will you do with a gallon of mineral spirits if you end up not liking oils?
Brush Tank You may be able to get this a few dollars cheaper at a local art store
Linseed Oil (slow drying) or Alkyd Medium (Most things will dry overnight. I find Liquin a little smelly, but it's the most popular. There's also Galkyd and Neo Megilp that will do the same thing)
For a palette, I use the glass out of a picture frame with paper taped to the back and the edges taped. Easy to scrape clean with a razor blade. Good quality palettes are kind of expensive for what they are, so I'd use the money elsewhere. There's also disposable palette paper
Taklon brushes. Brushes are by far the least important supply to splash out on. I use Hobby Lobby store brand bundle packs when they're half off, and they work just as well as anything else. As long as it doesn't look like those scraggly kid's craft set brushes, they're fine. Taklon are great all purpose brushes to get you started.
Paint knives Mix piles of color using these first to prevent pushing paint down inside the brush, they'll last longer. You can also experiment with knife painting.
Canvas Panels These are my favorite surface for just getting started. Cheap, easy to store, you won't feel pressure to make a good piece every time and yet they're able to be framed if you want. The ones that say "watercolor" tend to have a smoother surface. If you have a Hobby Lobby nearby, you can get smaller bundles for a bit less money.
Hope this helps! I think you can definitely come in under $100, or very close.