Does anyone have any recommendations for a second screen that's not as pricey as the 5k LG monitors?
Economy: yeah, 1920x1080 "Full HD" starts to look a bit chunky at 27" when viewed at desktop monitor distances. Instead, if you don't want to pay for 4k/5k, look for a 27" 2560x1440p (or "QHD") display - that's the resolution that the 27" iMacs used before they went 5k, and the icons/controls etc. will all be the same physical size as on the iMac screen in in default mode.
4k: not
as sharp as the 5k screen but still pretty good and vastly better than 2560x1440. Will default either to native resolution (tiny text and icons strictly for younglings with 20:20 vision) or "looks like 1920x1080" (big icons and text, but very sharp) but in displays preferences you can choose a scaled "looks like 2560x1440" mode which will pretty much match the main iMac display.
Note that once you go to 4k and beyond, the "scaled mode" options are nothing like any past bad experiences you may have had of using standard def screens at non-native resolutions. "Looks like 2560x1440" means that the image is rendered internally at 5120x2880 (5k - same as the iMac) and then downsampled to 4k for the display - the result is far sharper than a regular 1440p display and the icon/system text sizes match the iMac in default mode.
Technically, the non-integer "scaled modes" are less optimal than the "pixel doubled" modes (looks like 1920x1080 on 4k) and place more load on the GPU but you'd have to go looking for the quality difference and you can always switch mode if you're doing GPU-intensive work.
FWIW, I have a Dell S2817Q 28" 4k - the colours are too weak for serious graphics/photography work and the stand/ergonomics/controls are poor but its at the low end of the price range, pin sharp, good viewing angles and perfectly sound for general-purpose work. I got one because it was in stock at a local store for a non-insane price when I wanted a display, and feel like I got a decent deal. Currently sitting on top of a copy of "Electricity and Magnetism by Bleaney and Bleaney (other basic Physics texts are available)" to bring it up to the same level as the iMac display (which doesn't cover itself in ergonomic and adjustable glory either).