If one has the Proficiency then Shields come with no drawbacks nor requeriments.
If multiclassing from Rogue into Fighter you will get Medium Armour and Shield proficiencies. For Humans Shield Proficiency is a Race ability. If you want Heavy Armour either start as Fighter or buy it as a Feat (comes with +1STR).
A 6/6 anybody/Fighter split gets you 3 Feats (the usual for running a straight Class), due to Fighter having an extra at lvl 6.