if HEAVY cooking (like maramihan na pang-fiesta, hehe) and no nearby window or door, you really need a strong ranghood but also make sure na may provision for this kasi hindi siya basta-basta kinakabit. otherwise, filter-type hood is fine.
as for the kitchen splashback, if you have the range with cover, no need for splashback. if cooktop lang, i suggest you install one kasi sa likod lang ng cooktop area and not sa buong kitchen. the reason for this is to prevent wall stains from the (food) oil and maiwasan mag-bubbles ang wall paint from the heat of the cooktop.