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Tiny Titans is very cute and tells adorable stories, from what I've read of it. They do tend to be full of in-jokes for long-time DC Comics readers, but on a surface level, most of the stories can be easily understood as friendship type stuff without knowing who most of the characters are.
Parts of the runs of Superman Adventures, Batman Adventures, and Gotham Adventures are excellent and highly recommended. They were tie-ins to the DCAU animated series, and some of the first non-Archie/Asterix/Tintin comics that I ever read.
Best of the lot is the Ty Templeton-written run of Gotham Adventures (first 13 issues or so, IIRC; it's a shame his Batman & Robin Adventures, which were arguably even better, aren't similarly spotlighted with a 1st-issue introductory freebie), which told very thoughtful and imaginative stories, often with great emotional depth, built on the DCAU framework and trying to explain the changes in the cartoon style from B:TAS to TNBA by framing the art redesigns in terms of character development. It's a rather mixed bag after he was forced off the series due to editorial interference, but there were still some generally fairly decent stories (but I'd advise saving your money on the non-Templeton issues until you're feeling flush and indulgent).
In an extremely close tie for the top spot (B:GA got bonus points because I'm much more interested in the Batfamily than the Superstuff), Superman Adventures had some of Mark Millar's very best writing ever, and if you're interested in the character at all, you shouldn't miss his issues, which were truly excellent and thoughtful examinations of what it meant to be Superman and live in his world. They're somewhere around the 20s-40s of the run, IIRC. The first 20 or so issues written by Scott McCloud and other people are also quite good. After Millar, there's a few good issues by Templeton and others, but otherwise a rather steep quality drop.
The entire run of the early 90s Batman Adventures with the Rick Burchett art (I think they've misattributed the writers, since I'm pretty sure Ty Templeton & Dan Slott didn't show up until a later reboot of the series) is generally of fairly high quality, albeit a little more tightly tied into the Batman: The Animated Series tv show in terms of referencing characters and plots that first showed up there, and the writing is maybe a little retro in feel. Still, the stories are fairly good and should be easy enough to follow.
All the Adventures titles have good stories with not too much violence or very dark themes (some of them are a little moody, having to do with various Batfamily members' parents' deaths and all), truly suitable for all ages without being dumbed down for the kiddies.
The old Impulse run is really pretty good for the first 26 or so issues, which were written by Mark Waid himself (then the premier Flash scribe), and they're good clean light fun which I recommend if you have no objections to the art style (apparently something of an acquired taste for some Gentle Readers). After Waid's run, the quality was not nearly as good, from what I've read of the following issues.
Similarly, the Peter David run of Young Justice from the late 90s-early 00s is also highly recommended as a mostly fun and light-hearted book (with occasional surprisingly deep serious moments), but again, some people were off-put by the exaggerated cartoony art style, so YMMV. It's much more suitable for teen readers, IMHO, and has more mature themes, although it's also very, very easily enjoyed by grown-ups as well.
Teen Titans Go! told cutesy but not that deep stories which were fluffy light fun, probably best enjoyed if you've seen either of the TV cartoon series.
Personally, since most of the DC "kids" comics are still at the regular price of 99 cents which they've apparently set to lure in the younger readers on a regular basis, I'd advise picking up the Tiny Titans and other GN collection volumes that are actually on sale, and checking out the three freebie issues of PAD YJ, B:GA, & SA, and deciding later if you want to pick others in those runs up (although it does seem that the later PAD YJ issues starting in the 20s are genuinely on sale at half-price, and it's only the first dozen-and-a-half issues that are at the 99 cent introductory mark).
Hope this helps!
ETA: It turns out there is indeed a freebie Batman & Robin Adventures issue that was hiding at Comixology for you to try:
Batman & Robin Adventures (1995-1997) #21
ETA 2: And one from the reboot of Batman Adventures that was the actual Ty Templeton run as well:
Batman Adventures (2003-2004) #1
Enjoy!