Be aware that custom level packs are generally more difficult than the official games. However, if you're willing to look into playing custom level packs, especially with eric's remakes and conversions to Superlemmini, I recommend beginning with Dovelems. It has a really nice difficulty curve from start to finish, and is generally easy throughout, although there's still a few real nailbiters, especially in the later ranks. It was the very first custom level pack I played when I found out about Lemmini.
I can also recommend Dodochacalo's other mini packs too: Franlems, Dodopack, and Cachapack. The former is a pack of 40 levels entirely in French (I believe eric translated it all to English when he converted the pack to Superlemmini), while the latter packs are each 10 levels (20 levels total). These 3 packs are more difficult than his Dovelems pack, but they should still be manageable. Pimolems is another well done pack that's slightly harder than Dovelems, although I say the real difficulty starts at the third rank and stays high until the end of the 4th rank. The remaining ranks are special ranks and a bonus rank.
Then, if you're still willing to tackle even more packs and looking for a real challenge, Reunion is a highly regarded pack that has a nice difficulty curve throughout that's considerably harder than all the packs I mentioned in the previous paragraphs. The pack gets difficult much faster than the original game does. It already starts getting difficult near the end of the first rank. After the other packs I mentioned, this was and still is the largest custom pack I have ever completed, at a total of 150 levels. Also, all the packs I mentioned, including Reunion, I first completed on Lemmini. Reunion took me about 3 months to complete. Definitely not for the faint of heart or for the easily frustrated, but if you're willing to take on the pack, it's readily available for download.
These are all just suggestions, of course. You're more than welcome to start with the harder packs first, but if it's been a really long time since you last played Lemmings (I don't know your history, so I don't know how long it's been since you last played the game or if you have played any custom level packs), I would definitely start with the official games (Lemmings, ONML, Holiday Lemmings, etc) first, followed by Dovelems if you want to play custom level packs. Even without brushing up on the official games first, I say that it's still viable to start with Dovelems, as it does ease you into the game again with tutorial levels for the 8 classic skills, followed by easy puzzles.
I've played and completed all of the packs I mentioned, so that's why I'm able to offer my views on the difficulty of each. In any case, there's so many level packs to play and enjoy that it'll take a long time to get through them all. What's more, more are being made all the time, both from the veteran players and new, so the amount of content continues to grow all the time.