Need recommendations on quality, sturdy (hard), lightweight, wheeled luggage that I can pack my 50lbs in. Don't want to pay big $.
You have asked for an impossible recommendation. Good luggage is expensive, cheap stuff will wear out faster and require more frequent replacement. The choice depends on your usage but I lean toward the expensive stuff that lasts.
Keep in mind that in Europe you'll deal with small buildings, small elevators (sometimes no elevators), cobblestone streets, etc. Backpacks and duffels can be a gamechanger in places like that vs. rolling bags, and if carrying it you'll want to pack light.
I disagree with the poster above on TravelPro, mine have been great, best luggage I've ever owned. I own the Crew 8 line, which is obsolete at this point. I've only had to replace one handle in 10+ years for the two bags I own. The ability to replace parts vs. buying a whole new bag is now a requirement for me, and that typically is not an option on cheaper bags. I prefer roller bags over spinners because fewer wheels means fewer parts to break, and wheels infringe on the interior dimensions a bit so it gets you a slightly larger bag. You'll notice that many airline crew members use TravelPro bags, although that may be due to airlines forming a contract with them vs. personal preference. Airline crews also don't check bags and carry ons don't get nearly the same level of abuse.
Briggs & Riley is another great brand because they have an unconditional lifetime warranty. I believe they are the only company that does this, but it comes with a high price tag. Another uncommon feature is they put the telescoping handles on the outside of the bag. This creates a flat, square storage compartment but also means that has smaller interior dimensions vs. competitors because the outside dimensions are what has to fit in the airline's required dimensions.