I think you ought to look into a good pair of binoculars as well. I’ve owned both; a 76mm (3 inch) refracting telescope and a couple different sets of binocs - 9 X 55 and currently a pair of Swift 8.5 X 44 birding glasses.
I found the scope to be marginally satisfying, mainly because of the giant pain in the ass it was to set up and point correctly - this was in the days before the microchip and computerized equatorial mounts became available. Finagling with star charts and the polar and declination axes proved more than I could bear. I just wanted to look at Saturn, dammit. (I ended up giving it away). Nowadays you can just punch in the coordinates of any celestial object you’d like to view, and providing you’ve lined the scope up properly you can be reasonably assured you’re looking at what you think you’re looking at. (Although you’re not going to get that type of motorized equatorial mount for 2 or 300 bucks, let alone with a telescope).
On the other hand, binoculars are incredibly easy to set up and operate. I find the stereoscopic quality of the image to more than overcome the relative lack of magnifying power. After all, light-gathering is what we’re after, and telescopes of any variety ignore 50% of a human’s optical aparatus - that other good eye that’s hanging out there in the breeze.
Whatever you do, invest in a good tripod. People are constantly amazed at the image clarity that can be obtained via my birding glasses when mounted solidly. Most people are familiar with the shake induced when hand-holding binocs, and have never looked through a pair that were fixed in place. This becomes especially important the higher in magnification you go. The 9 X 55’s I owned were practically useless as a hand-held device, yet I could easily discern the rings of Saturn or count many of Jupiter’s moons by throwing them on my camera tripod.
I guess it’s a question of what you want to do with your image. Photography? Gaze at deep-space objects? A scope and mount that will do these activities justice will not be had for the amount you mentioned. Poke around the planets and moons, see mountaintops jutting into the sunlight from the dark side of our moon’s terminator? Binocs can easily satisfy those demands and also give you and your boy the ability to zoom in on more terrestrial delights such as the neighbor’s bedroom wind// oops I mean sporting events and the like.
Here’s a link that explains the choices much more comprehensively: