There are a couple of options for you. Carlos' answer above is absolutely correct. The FARs are helpful, as is AC 90-66A. You should take a look at both of those. AC 90-66A is informative, but not regulatory, and Part 91.113, 91.126 are regulatory but not particularly informative. 91.103 says you have to know everything about everything, which is true, but again, not helpful.
First the rules: Be safe, be alert and then proceed. FAR 91.113(c) governs your low fuel question. If you are below minimum fuel, and are in distress you have the right of way. There is a difference between a fuel emergency, which is "I'm going to run out of gas unless I land now" and a minimum fuel advisory/situation which means, I got just enough gas to get where I'm going and get myself safely on the ground. If your fuel status is in doubt, it's an emergency. Better to fill out that paperwork than the NTSB paperwork.
The other pertinent part of 91.113 is Aircraft, while on final approach to land or while landing have the right-of-way over other aircraft in flight or operating on the surface, except that they shall not take advantage of this rule to force an aircraft off the runway surface...
So, this means that the airplane on the final segment does have the right of way, over everybody but the emergency, but can't abuse the privilege. So, if someone wants to disrupt a busy pattern with a long straight in final, it's legal, and traffic in the circuit do have to give way and turn the base behind him.
Next, FAR 91.126(b)(1) which says all turns shall be left hand in the traffic pattern, so plan left traffic unless the AFD (US) advises the traffic pattern is right hand turns.
AC 90-66A tells us to play nice in the pattern. "It says Landing and takeoff should be accomplished on the operating runway most nearly aligned into the wind. However, if a secondary runway is used, pilots using the secondary runway should avoid the flow of traffic to the runway most nearly aligned into the wind." (AC90-66A 8. Recommended Standard Traffic Pattern, (f)). 8 a. of the AC states, "Prior to entering the traffic pattern at an airport without an operating control tower, aircraft should avoid the flow of traffic until established on the entry leg."
I have seen pilots arrive at an airport with a busy stream of departures call and declare they were landing on the opposite direction of the departure runway. They only have the right of way, if they are on final, but it doesn't strike me as a a nice thing (or safe thing) to do.
In a busy pattern, it is generally best to follow the AIM recommendations in the US, which is, unless otherwise noted, cross overhead the field and plan a 45 degree left downwind entry to join the traffic flow, watching traffic for spacing. If in doubt, break off and try again. Announce your intentions and position on the CTAF at all times, but be vigilant, as there may be some airplanes that do not have radios. Which also means they will not be seen on TCAS/ADS-B or whatever. It's probably a good idea to get an ads-b in receiver if you don't have one. There's a homebrew one based on a raspberry pi that can be put together cheaply and mostly works. Don't assume it will see all airplanes at all times.
Finally, once in the pattern go with the flow. If the pattern is too full for your comfort, the general rule is to remain at least 500 ft above the pattern altitude and move away from the flow of traffic, but there may be others doing the same, so watch and listen. Depending on the situation, you might want to divert to an alternate, nearby airport, buy some gas aand hope the pattern traffic is more to your liking when you come back. Turn your base only after the next airplane in line has crossed abeam you and adjust your pattern accordingly.
You might want to practice with an instructor who has some experience in high density traffic areas before you go on your own.