TLDR: Ninja Garb or Emergency Shell for New players, Necroshield Suit for veterans
When you start playing, use whatever armour gives you the most health regardless of the type (e.g. if you got a Rare or Epic armour from a chest) - because of the way Defense is calculated and because you don’t have much in the way of Melee & Ranged Resistance permanent upgrades, the difference between Body / Tactical / Heavy is negligible (the 10%/20%/30% is a boost to your Resistance, not protection against damage - details here), and while Ninja can give you more Dodge and Necro can absorb 1 hit (renewed every 80 kills) neither will compensate for the reduced Health.
As you progress through worlds, you could get a small edge by selecting Body / Tactical / Heavy Armour to match the world and/or the enemies you find difficult to kill. However, unless LightHeart adopts this idea to make Melee/Ranged Resistance and Armour to act as a percentage defense (and maybe even if they do), at higher levels in the Tournament and Endless event they will be useless, and any coins spent on upgrading them will be money down the drain.
My recommendation is to make Ninja Garb your main armour and focus on levelling it up - the 7% dodge it provides would more-or-less double your chance of dodging hits.
I don’t consider the Emergency Shell a good investment in the long term (reasoning) but if you do get it, you could use it instead of the Ninja.
Either way, in the meantime, fuse up any NecroShield suits you get as well (don’t level it up yet unless you have coins to spare) - as you progress you get other sources of Dodge (Mr. AutoFire at Level 20 and 50, likewise Jackbot if you are able to unlock him, and Firebug’s 10% is also very handy) which reduces the impact of the Ninja garb (an extra 7% is a big deal when you only have ~5%, but not much of an improvement if you have ~35%) and you should be getting more skilful at evading hits, so eventually you will switch to the Necro.
Note that developing multiple armours can eat up a lot of coins (details), so unless you have the Metal Detector or buy the Battle Pass regularly, you are probably better off going with the Necro from the start.
19/02/2022: Updated to include Emergency Shell