Frigkas - Culture has basically nothing to do with military expansion. It can be can be achieved 100% peacefully.
Only reason to fight in CV is if you were tight for the recommended number of cities and wanted to capture a few more good ones. Sometimes it can be good early to capture 1 or 2 nearby AI capitals as they might be cities for CV or in general. Also, you might want to capture certain culture friendly wonders. OR you just might fight some war for fun and gold.
Otherwise, on normal/standard, expand to 9 cities, build cottages in your cap and maybe 1 or both other L cities, build temples to build cathedrals (or like) in L cities, Lib>Nat, Build Taj, run artists, raise culture slider to 100%, win. Last tech you probably ever need is Printing Press after Lib>Nationalism.
Civics (Rep/HR, Bureau>Free Speech, Caste System, Merc, Pacifism)
Wonders:
Any Great Artist producing wonder is good if you can build it quick (bonuses or forests)
Parthenon
Sistine Chapel (definitely want this one)
Taj (GA producing wonder on your direct beeline that provides golden age which boosts culture...save non-Great ARtist great people for late golden ages as well)
National Wonders:
National Epic and Hermitage (in cap) are really the only two NWs you need. If Heroic Epic is cheap it may be worth building in GP farm as it does produce GA points. Ofc, you have to fight to activate it or just try to get a warrior to Woody3 against barbs. HE not necessary though
Read Jesusin's guide in War academy and practice..one of the best guides in the war academy by the best CV player.