1. The Little (Pinky) Finger

This is often the first choice for a man who wants to wear a “statement” ring.
Pinky rings have a couple of advantages: they don’t have religious or cultural associations in most cultures (unlike the ring finger), and, like rings on the fourth finger, they don’t touch or interfere with the index/pointer finger at all.
It also isolates the ring from your body a bit, making it more of an eye-popping statement. As a result, pinky rings tend to be among the “busiest” or flashiest of designs. It’s where you wear things when you want attention paid to them.

2. The Fourth (Ring) Finger

In the US and much of North & South America, the ring finger is most commonly associated with wedding symbolism: a band on the right fourth finger indicates engagement, while a band on the left fourth finger indicates marriage.
That said, nearly all men opt for a simple gold or silver band for their wedding/engagement rings. A large ring with a jewel or a three-dimensional design on it is far less likely to be taken for something related to your marital status.

3. The Middle Finger

Apart from the obvious hand gesture, the middle finger is your largest, boldest finger.
Rings worn on the middle finger are surprisingly uncommon — in part, that’s because it’s adjacent to the index finger, and anything bulky can be quite a hindrance to fine manual tasks. It’s best to keep things small and simple if you’re wearing them on your middle finger.
That said, a lot of first-time ring-wearers might feel more comfortable with the middle finger, purely because if feels so central, sturdy, and frankly, “manly.” If the idea of a pinky ring weirds you out, and you don’t want any confusion with wedding/engagement symbolism, the middle finger’s a safe default.

4. The Index or Pointer Finger

There’s a natural instinct to keep the pointer finger clear, since we use it more than any other digit (except the thumb), but it turns out that a ring on the finger doesn’t interfere with it as much as one on the finger next to it.
If you go back hundreds of years the index finger was the most common location for a man’s ring (generally a signet or a crest — in some parts of Europe, people below a certain rank were actually forbidden from wearing rings, because they denoted specific family status).
That makes the index finger a good place for things like class rings, fraternal rings, or family and membership crests, although many men (especially younger, unmarried men) opt for the ring finger out of habit instead.

5. The Thumb

Thumb rings have a slightly outlandish feel to people who come from conventional North American culture, but they’re actually reasonably common world-wide.
In most societies a thumb ring on a man is a sign of wealth or influence, and they tend to be broad or bulky to reflect that (also to fit comfortably on the thumb, of course).
A thumb ring is also often the natural choice for men who want to wear multiple rings on the same hand, since it’s at least somewhat distanced from the others. A wedding band plus a pinky or middle finger ring can get quite crowded, both visually and physically, whereas a thumb ring gives everything some space.
Thumb gestures are associated with interaction and friendship (think “thumbs up”).

Does the ring on the right index finger indicate searching or what?

I didn't know that rings on different fingers had a specific symbolism. I was curious to explore this a little more because I've hardly ever worn rings in my life, except for butterfly promise ring. And I decided to do an experiment: on what finger and on what hand would it be most comfortable to wear a ring. It turned out that it's uncomfortable to wear on the index finger - often, it slips off and gets lost. It's also annoying to wear a ring on the middle finger. It's the same with rings on the thumb - the feeling when you wear it is not so pleasant. But on the ring finger is convenient to wear a ring, as the ring fits tightly against the skin and does not move.