most airlines have their own frequent-flier program (you mention LH with miles&more). Some 'other' arlines are close partners (for LH thats all StarAlliance airlines) from the airlines you list LOT, Eurwings and Air Canda are partner of miles and more and you earn (and can spend) miles flying them (also United Airlines, etc. etc.). British Airways is not (their major partners are the oneworld-members).

To become a member of a frequent flier program you don't need any credit-card. The airline-program of your choice will send you, after application (often a provisory card can already be tearedoff the application form) their card home.

Most programs differ (even between airlines of the same alliance) heavily: diffent mileage earning and spending rules and mileage-amounts. Different upgrade- and lounge-access-policies, different miles needed in different periods to climb up the 'status'-list for that specific frequent-flier program.

To give you better individual advie, which program(s) might be the best for you, we would need more informations: your place of origin (programs often have also different rules for different countries), kind of fares you buy (eco, business, first), what are priorities for miles-usage later (free award flights in which class from where to where, class-of-flight upgrades on paid tickets). Etc. etc. etc.