As Ajax was saying, Aperture is the size of the hole at the top where the light comes through and it is way more important in telescopes than magnification. It is very important for brightness and clarity. But, you have to double the aperture diameter to make a significant difference. A 12" telescope is about the biggest that you are going to want to take anywhere by car. Focal length is the length of the telescope, specifically the distance from where light enters to where the image is formed. This is achieved differently by different types of telescopes. The focal ratio is the focal length divided by the aperture and is probably the most important number in telescopes. Te f ratio of most telescopes usually ranges from F/4 to F/14. Lower ratios provide a wider field of view and are preferred for astrophotography. Higher focal ratios have a narrower field of view, but higher magnification, so are preferred when looking at planets. You can see Saturn with 50X magnification, but it takes 150X to see the rings. You can see Jupiter with 200X magnification. The maximum effectiveness for an eyepiece’s magnification is about 50x for every inch of your telescope’s aperture. The smaller the focal length number on an eyepiece, the greater the magnification. The largest focal-length eyepiece you can use is calculated by multiplying the focal ratio by 7. You also have to consider exit pupil size. Exit pupil size = aperture / magnification or eyepiece focal length / f ratio. It's best not to go lower than .5. So with 130mm or 5.1" telescope, it is best not to exceed 260X and with a 102mm, it's best not to exceed 204X.
Refractor telescopes are the historical pirate type of telescope. They have a lense at either end of the focal length and tend to be longer and slightly more expensive than Reflector telecopes. Reflector telescopes were invented by Isaac Newton and use two mirrors, a primary mirror on the bottom which reflects to a secondary mirror which creates the plane of view. A variation on the Newtonian reflector is the Dobsonian reflector which instead of using a tripod, use a mount with a lower pivot point for a lower center of gravity than a Newtonian on a tripod. Reflector telescopes give you the most for your money, but they do have some drawbacks. Then you have the Cassegrain, aka compound, aka catadioptric telescope which is a hybrid of the two previous types and uses a combination of a mirror in the back and a lense in the front. There are two types of Cassegrain telescopes, Schmidt-Cassegrain and Maksutov-Cassegrain. There seem to be more Maksutov telescopes for sale, but I don't really know which is better.
Then there are mounts. There are three main types. The first is like a photo camera-style mount, but reinforced with blocks or rings, this is known as an altitude-azimuth or alt-az. The Dobsonian mount is a variation on the alt-az. The second is the equatorial mount, these are set up by lining the mount with the North star and then they only turn on one axis, not two like the alt-az. Equatorial mounts are better for looking at planets or for astrophotography. Finally, the go-to or motorized mount is hot right now. They have a handheld controller that lets you pick the celestial object you want to view. Unless they have gps, you have to go through a set up procedure that takes several minutes. I think the technology will get there, but at present the money would be better spent on a better telescope and eyepiece.
Newtonian Reflector telescopes usually have an open tube, so their cool down time is quick. Having the temperature at ambient temperature is important for planet watching. Due to its wide angle of view, you need to use quality eyepieces. The mirrors can get bumped out of alignment. It only takes a couple of minutes to fix, but you should find someone to teach you what to do. 6" and larger Refractor telescopes are the bees knees for looking at galaxies, nebulae and planets. They are not as well suited to astrophotography as Cassegrain or Refractors. They have an open tube, so dust and other things can get inside.
Cassegrains are more compact, comparably 1/3 the length of Newtonian, and make for a good all-purpose telescope for deep sky viewing, planetary viewing and astrophotography. They are relatively maintenance-free. They are usually more expensive than Reflector telescopes, but usually come with motorized goto functionality. They have a closed tube, so they take longer to adjust to ambient temperature.
Refractor or the traditional style of telescopes have excellent image quality. You are going to want at least a 3" aperture to see Jupiter or Saturn. Refractors get expensive when you go larger than a 4" aperture and require expensive mounts. You would want to get one that is apochromatic. This fixes an issue, where some objects have a light-ring around them. They are sealed and relatively maintenance-free.
Eyepieces are very important. There are several different types, but the three most common are Plossi, Orthoscopic and Kellner aka MA. Plossi eyepieces are the most common, are relatively inexpensive and are a good all-around eyepiece. Orthoscopic or Abbe eyepieces have a narrower field of view, but produce a better image and are a better choice for lunar and planetary viewing. Kellner eyepieces use a three-element design, that is they have three lenses. Kellner also known as "MA" (modified achromat) are a budge eyepiece that can turn in a good performance with scopes of long focal ratio, such as Cassegrains and refractors. They do not work well with telescopes of short focal ratio. Eyepieces in the 2 - 4.9 mm range work better with refractors and Cassegrains. 5 - 6.9mm eyepieces are good for planetary viewing in long focal length telescopes. 7 - 9.9mm eyepieces are good for planetary and lunar viewing in short focal length telescopes. 10 - 17.9mm eyepieces are good for viewing galaxies and nebulae in all focal lengths. 18 - 24.9mm eyepieces are good for galaxies viewing in short focal length telescopes. 25 - 30.9mm eyepieces are good for locator eyepiece , nebulas on longer focal length and lunar viewing on shorter focal length.
So what do I recommend?
The cheapest decent Cassegrain is the Celestron NexStar 127SLT at $550:
https://www.amazon.com/Celestron-NexSta ... uage=en_USIt comes with a motorized go-to mount. It has a 1500mm focal length, so with a 5mm eyepiece, you should get 300X power.
The cheapest decent Refractor is the Explore Scientific FirstLight Tube Refractor AR102mm at $329:
https://www.opticsplanet.com/explore-sc ... te-2064156It has 1000mm focal length and a 4" aperture. It comes with a 25mm eyepiece and an equatorial mount. With a 5mm eyepiece, you should get 200X magnification.
The cheapest decent reflector is the Orion 09007 SpaceProbe 130ST at $310:
https://www.amazon.com/Orion-SpaceProbe ... uage=en_USThe 130ST has an 5.1" aperture and a 650mm focal length. It comes with 10mm and 25mm eyepieces and an equatorial mount. For $93 you can add a Celestron X-Cel LX 5 mm eyepiece which should give you 130X magnification.
https://www.amazon.com/dp/B005OP1EJM?ta ... th=1&psc=1If you are able to spend more, the Celestron AstroMaster 130EQ at $597 has a 5.1" aperture and 1000mm focal length. It comes with 10mm and 20mm eyepieces and an equatorial mount. Pairing it with a Celestron X-Cel LX 5mm eyepiece would give you 200X magnification.
Instead of a viewfinder, use a 32mm eyepiece. This one at $99 has a 70 degree field of view:
https://www.amazon.com/dp/B000M89H72?ta ... planets-20 The apertura is nice too:
https://www.highpointscientific.com/bra ... iece-swa32It will also be a good idea to get an eyepiece in the 15-18mm range and a Barlow lense. A Barlow lense is paired with your eyepiece to double or triple your magnification. Depending on the celestial object you're looking at and sky conditions, sometimes these are a nice addition.