Keep in mind that your dwarves can carry up to a certain amount (which is strength/size dependent) without being encumbered at all.
Based on the numbers given in the arena for speed, as well as my experience from adventure mode, a full suit (helm, breastplate, mail shirt, greaves, gauntlets and high boots) of steel or iron armor does not encumber a dwarf at all. If you instead make the armor out of copper or bronze (which are about 1.5 times as heavy) they will be somewhat encumbered, but I don't think steel armor plus any ordinary weapon is enough to slow them down. Also, military training rapidly increases size and strength, so I doubt any of your military will have a problem. The only way you would have an issue is if you use copper/bronze armor, or with marksdwarves, as bolts are stupidly heavy.
Using wood/leather shields is a good idea, as they are lighter and functionally identical to metal shields [Edit - identical for defense. As pointed out below heavier metals are better for bashing, but shield bashing is a terrible attack anyway].
If you want to test if your dwarf's equipment will slow them down, just put it on a dwarf in the arena, assume control, and see if the dwarf's speed is still 1.0. The only potential issue is that both fortress and arena-created dwarves have some variation in size (and hence carrying capacity), but assuming you train your dwarves at all they will be above average size.