NOTE: this is my opinion, not law, take these suggestions as such. I won't be including OPs as that's a given
-Cho' Gath - A Tank with a safe laning phase AND kill pressure. Cho'Gath's passive grants great sustain, and Cho'Gath is a very simple champ to play, both fantastic strengths for Solo Queue. He also doesn't have many poor matchups so he is a great Blind Pick, and forgives mistakes thanks to great CC and sustain.
Honorable Mention - Vladimir, Swain - Both have their bad matchups, but pack sustain to help you make dat mad CS gold. They pack good damage and can contribute well at most stages of the game.
-Shyvana - One of the best jungle clearers in the game makes stacking Devourer on her a breeze, and allows you to turtle in your jungle if you aren't a good jungler and get insane gold from farming. You can gank early if necessary, you can counterjungle some opponents, the point is, you have OPTIONS. both in playstyle and build path.
Honorable Mention - Amumu - doesn't turtle in jungle as well as Shyvana but has an easy to grasp kit, but is vulnerable to invades and early ganks rely on Q.
- Lux - I'm noticing a trend here. Lux is a very safe pick, her insane range and crazy damaging ult allows her to artillery down opponents and stay far back in lane to avoid ganks. She also is a strong pick against some of the strong mids right now, like Veigar, simply because she outranges most of them.
- Vel'Koz - Somewhat less safe than others, but packs versatility. Vel'Koz's laning is strong thanks to spammable spells, low Mana Costs, and his passive. He also can itemise for poke, with Rylais and Liandries, or burst, with Ludens, Rabadons etc. His ult gives him teamfight pressure and he doesn't fall off anytime so you always have the opportunity to succeed.
Honorable Mentions- Lissandra, Ekko - Both have few bad matchups, and can save themselves to prevent you from feeding your opponent. Both also are good vs assassins who are so popular in Solo Queue.
- Caitlyn - Counters Vayne and Jinx to an extent, both are whom are common picks. Her insane range makes laning safe, as well as teamfights, and as long as you go off the rule: Your weak until 4 items outside of laning, don't be aggressive, you should do fine. Excellent to learn ADC with.
Honorable Mention - Ezreal, Tristana - Both are very safe, although Trist has that monster late game if you like that sorta thing.
- Thresh - Obvious, he has several options in his kit, is tanky, and can save your ADC in lane so you can make up for allies mistakes. You have options to be aggressive with hooks, of defensive, so your ready for most lanes.
Honorable Mentions - Braum, Alistar, Tahm Kench - Tank supports are harder to kill and these 3 can save the ADC to prevent allies feeding.