Should you choose a refractor telescope over a reflector telescope?
Yes. One of the main benefits of using a refractor telescope is that it is simple to use. This makes them ideal for beginners. No calibration is needed for refractor telescopes. Also, with a refractor telescope, the image is viewed correctly from top-bottom and left-right using a star diagonal; the image is not inverted in any way. It can also make a good daytime spotting scope.
Refractors generally have the edge over reflectors for quality images, both from the standpoint of lens and mirror quality, precision optical mountings, and lack of central obscurations.
Reflector telescopes need to be calibrated before use. Sometimes calibration can take a long time, depending on how knowledgeable you are with your adjustments on the telescope.
Due to how reflector telescopes are made, they do not use star diagonals. Be prepared to look through the telescope to find that the image is inverted.
Do note: Sometimes people donate telescopes to Goodwill. I was lucky enough to get two at a bargain. They were, of course, two reflectors. Granted, it was dirty, etc., but I cleaned it all up piece by piece and tested them out. For me, the bargain ones at Goodwill thus far are only good for viewing the moon. And yes, the image is inverted (either right to left or bottom to top, or both, I forgot), which I am not used to viewing. For the unbeatable price, I cannot complain.
Should I get a computerized telescope?
It is up to you and your budget. Computerized telescopes function by way of a motorized mount that controls the positioning of the telescope as it points toward the night sky. They are programmed to easily view objects in the sky and to automatically follow the object and center it in the eyepiece for easy viewing. They are very expensive, and if something malfunctions or breaks, it can be very costly to fix and, in some instances, not even functional until it is repaired. Once you can set one up, I assume it should be smooth sailing. I only have experience with manual operated telescopes.
Alert, please understand: Most objects that we view in the night sky are always moving. Let's say we are 500 feet away, standing still, and looking at a red car that is moving to our right. We can keep our eyes on the red car as it travels to the right of our viewing eyesight for quite a while before eventually having to rotate our head to the right to keep the red car in our line of sight. But if we were to stand still and view the red car much closer, say, 30 feet, we would need to rotate our heads much more quickly to the right in order to keep that car in our line of sight. This concept is the same when using a telescope. When you zoom in very close to an object in the night sky, you will continuously need to make adjustments in order to keep that object viewable in your eyepiece. Thus, for computerized telescopes, they do the slow rotation adjustments to follow the object for you automatically.
I hope this helps to understand. When you first look into the night sky to view an object, it is better to zoom out in order to have that object in your eyepiece for viewing. When you have the object in view, you can then zoom in for a closer view (larger image). But you will notice that the object is moving from left to right in your eyepiece slowly, but at a quick pace. You will need to continuously use the fine movement adjustment knobs on the telescope in order to keep the object in view every 30 seconds or so. When you zoom out again, you can see the object longer before needing any adjustments, but the object will look smaller (a smaller image), depending on how much you zoomed out. From experience, you will constantly zoom in and out (if you have a zoom eyepiece) while using the fine movement adjustment knobs in order to get "that great moment image" and keep it in view for as long as you can before starting all over. Once you get the hang of it, you will be able to quickly view objects in the night sky and also keep them in view for great "showings."
Can Earth's moon, Jupiter, and Saturn be viewed anytime during the year?
I guess with a powerful telescope or NASA's telescope, the answer is "yes." For the average telescope, the answer is "no." At certain times during our Earth's year, these objects rise in the daytime and set in the evening before anyone can view them. Because the sun is out or it is not dark enough, these objects cannot be seen through an average telescope. And when these objects rise late at night, most of us are in bed. You can browse many astronomy websites to find out which month of the year is the best time to view these common celestial objects in your area.
Websites to learn more about celestial objects and astronomy:
https://www.timeanddate.com/astronomy/night/usa/fayetteville-ar
https://www.timeanddate.com/moon/phases/usa/fayetteville-ar