I'm not here to give my opinion on which fish to choose, but I will tell you that you need to have the proper care and devotion for a fish.
Before you get the fish, you will need to cycle the tank for 3-6 weeks. The Nitrogen Cycle is extremely important when it comes to owning fish and keeping them healthy and happy. You will need liquid test kits for Ammonia, Nitrite and Nitrate to monitor those levels during this process.
A Betta needs at least a 2.5 gallon tank (preferably larger) with a soft filter and a heater. There is no exceptions with bowls or anything smaller. In fact, a Betta would love the space in a tank larger than 2.5, but as I said, that is the smallest you can go. It's always best to buy the largest tank you can afford and the bigger the better.
Goldfish require a different set-up. One fantailed variety of Goldfish needs a 20 gallon tank with double filtration. If you are wanting more than one, you add on 10 gallons for every additional fish. They are big poopers so having double filtration is essential to keep the water clean.
Which ever fish you decide, just make sure you give it the care it's supposed to have.