From a safety point of view, I wouldn't have any issues flying the airlines you've mentioned.
AtlasGlobal, Pegasus - turkish LCCs. Haven't flown them. Reliability seems to be decent.
XL - French, haven't flown them.
Level - a brand name for 3 separate airlines owned by IAG (owner of BA and IB). Reliability is generally good for the BCN-based one, in-flight product is an LCC one (Expect nothing and you'll be impressed). Good value premium economy. I haven't flown the ORY-based LEVEL yet nor have I flown ex-VIE short-haul LEVEL.
LOT - Polish, new 787s, reliability is generally decent. Nice lounge in WAW.
Ukraine Int'l Air - Ukrainian, reliability (on-time performance) is not great, long-haul flights are also not great. Short haul flights are good. New/newish planes all around.