Let's break this down....
RIMS:
Different rim profiles will impart different characteristics. A shallow rim will be more prone to radial flex than a deeper rim. While this can improve compliance, it's also more prone to permanent compression damage. The deeper rim will be harsh and chattery due to its poor radial compliance, but will handle big hits better. A wider rim will have better lateral stiffness than a narrow rim, however if the rim profile is wide and shallow, some of the stiffness will be traded off by the longer spokes and reduced brace angle to a given hub. Finally diameter. All other factors being equal, a smaller wheel is stronger, because there's simply less material for elongation forces to act on.
SPOKES:
Obviously heavier gauge spokes will have more strength. However, stress is concentrated at the ends of the spokes, and if there's not enough built-in flex to dissipate the stress, fatigue and breakage will occur. Butted spokes, which have a thinner shaft than ends, allow more stretch, which relieves stress from the ends. So you lose a small amount of rigidity, but gain a lot in durability. More spokes mean when a given load is applied to the wheel, the load borne by each spoke is lower, therefore greater overall load-bearing capacity. Tension needs to be adequate, appropriate for the characteristics of the rim, both material and profile (carbon needs higher tension than aluminium, shallower needs more than deeper), and even. Brass nipples all the way; there is no valid reason for the existence of aluminium nipples, and they're an especially bad idea in carbon rims.
(B) Lacing:
Radial lacing, being the most direct line from rim to hub, gives optimal vertical and lateral stiffness, but is unstable when rotational load is applied through drive and braking at the hub. Radial is fine with rim braking, because the brake load and the resistance from ground contact are both acting directly on the rim, with no force transferring to the hub. Disc and other hub-based brakes need rotational stability to transfer their force to the rim and ground, so crossed lacing must be used. On a given spoke count, more crosses equates to a greater deviation from the radial alignment for each spoke, therefore more efficient torque transfer and greater rotational stability, which in turn reduces stress on the spokes. However, lower spoke counts, by way of greater angular difference between each spoke, achieve the same thing, so you can get away with fewer crosses on a low-spoke wheel. I consider 28 spokes to be the crossover point between going 2x or 3x; more you go 3x, less you go 2x. If I was building a 28 spoke wheel, I'd go 2x for a rim-braked wheel, but 3x for a disc (or other hub)-braked wheel.
HUBS:
Wider-spaced and/or larger diameter flanges will increase the bracing angle of the spokes from the rim, which increases lateral stiffness. Bearings placed as close to the ends of the axle as possible will minimise axle flex; your opposing pairs of load points on the axle are the dropouts and the bearings. The further apart these opposing load points are, i.e bearings well inboard of the dropouts, the more the axle will flex and eventually break. Case in point the old hubs for screw-on freewheel clusters; the drive-side bearing is so far inboard of the end of the axle that about a third of the axle is unsupported, so has a very high probability of eventually breaking. You don't need four-bearing hubs, you just need two widely-spaced bearings. Cup-&-cone hubs also give better lateral support than cartridge bearings.
MATERIAL:
Can't go without some fuel for the carbon vs aluminium debate. Both have pros & cons. Aluminium is forgiving to an extent in that it (like other metals) has a phase where if it takes a hit it will bend but not break. Carbon doesn't have that phase; it's a lot more elastic than aluminium, so will spring back from a greater impact, but when its elastic limit is reached, it will break. Aluminium rims are softer against larger loads, like cornering and landing jumps, but are more rigid against smaller trail chatter. Carbon is the opposite, it's stiffer against the bigger stresses, but absorbs the little chattery vibrations a lot better. This stiffness is why higher spoke tension is needed with carbon; it tends to highlight the stretchiness in the spokes because the rim isn't absorbing as much of the stress, so you can get more tyre rub as the rim moves over the hub. Carbon has a vastly superior strength-weight ratio, so a carbon rim of equal weight to an aluminium one will be a lot stronger. In fact a subtantially lighter carbon rim will still likely be stronger than a benchmark aluminium rim.....
layball:
