The SL1200 has many fans here. When I've heard them, I wasn't overly impressed, but each person listens for different things. Years ago, Tone Audio compared the AT-PL120 (predecessor to the current AT-LP120-USB) to a stock SL1200 and liked the AT better. A reviewer at Sound & Vision compared his SL1200 Mk II to sub-$500 belt drives from Rega and Music Hall and liked the belt drive models better.
https://www.soundandvision.com/content/face-best-turntable-budget-page-4#VWwKqhHzOceXuiUC.97
What HiFi was liberal in its praise for the LP5, but also pointed out that the then-current Rega entry-level RP1 sounded better (and they like the new Planar 1 better than the RP1). I haven't seen a mention of whether you have a dealer to work with or not, but the best way to be sure that your money will actually be buying improved performance is to listen to options with your own ears before making a choice. With a different stylus or cartridge, you might be perfectly happy with your current turntable. Then again, through audition, you might hear a better 'table that you can't live without. If you don't have a good dealer to work with, all you can do is read reviews, gather opinion from sites like this, and make your best guess (and you can assemble a pretty fine system that way, too!).
Another thing to bear in mind is that just because something better exists doesn't mean you have to have it to enjoy your records. What HiFi made that point in their LP5 review. After noting that the Rega would be step up, they continued, "but it cannot detract from the AT-LP5’s musicality. Sonically, the RP1 has the edge you’d expect from a sole-purpose turntable, but when we switch back we are more than pleased to listen for the rest of the day without missing the extra detail or dynamics." Given that you want to stay away from belt drive options, you might prefer the LP5, or some other direct drive, even if you heard something that sounded a bit better in direct comparison.
Read more at
https://www.whathifi.com/audio-technica/lp5/review#wQHMMDLgq211HQ5y.99
I had a "sounds good enough" experience with my aging LP12. After decades of use, the main bearing was beginning to show signs of wear, and the dealer suggested that with a new power supply and motor to go along with the new spindle and thrust plate, my Linn would be ready to give another 20 years of great performance. On the other hand, even in its worn condition, it was worth more than enough on the used market to let me sell it and buy a brand new Rega RP3. I wasn't sold on the earlier P3-24, but the RP3 was an obvious advance, "contagiously musical" as one reviewer put it, with "a superb sense of pace and rhythm." In direct comparison, even my aging Linn was better, but the Rega still got my toes tapping. I play music just about every morning, and for the last few years I've been more than pleased to let the humble RP3 provide me with album after album of thoroughly engaging record playing.