For example, would cheaper & longer paths such as Hohmann transfers be favored, or will more direct (and therefore more expensive) trajectories be preferred?
Neither. Hohmann orbits are tangent transfer orbits between one circular orbit and another. Asteroid orbits can be decidedly elliptical. The transfer orbit would probably still be more or less tangent to departure and destination orbits. But it's path might be a lot different than the 180 degree path we think of as Hohmann.
To illustrate here's a pic of possible tangent transfer orbits between a circular earth orbit and an elliptical asteroid orbit:
Most the possible tangent transfer orbits are pastel but I've darkened the red one. You can see the angle between departure and arrival is 100ª or 260º -- quite different from a Hohmann's 180 degrees.
Also Hohmann orbits assume impulsive burns at periapsis and apoapsis of transfer orbit. Such impulsive burns are best done with high thrust chemical propellents. However chemical propellents don't have an exhaust velocity much over 4 km/s.
The Keck Report suggests a solar electric propulsion vehicle that uses xenon propellant. Low thrust but an exhaust velocity around 30 km/s. With a high exhaust velocity, we can impart some delta V to an asteroid without a huge mass of propellent. But these low thrust burns can take a long time to accelerate an object. A slow steady burn can result in spiral trajectories rather than elliptical orbits.
For this question we narrow the source of material to the main asteroid belt and assume that resource needs to be brought within Earths SOI.
A bad assumption. To lower a main belt asteroid to a 1 A.U. perihelion would take around 4 km/s. Delta V budgets would be way too high to realize a profit.
The Keck report talks about near earth asteroids that only require about .2 km/s to be parked in lunar orbit. This is doable.
It's interesting that Chris Lewicki is one of the co-authors of the Keck report. Lewicki is the chief engineer for Planetary Resources.
how important will it be for methods of transporting materials to Earth to become cheap?
One of the things that makes spaceflight so expensive is the tyranny of the rocket equation. With all propellent at the bottom of a deep gravity well, every spacecraft has a minimum delta V budget of around 8 or 9 km/s. But with a propellent source high on the slopes of earth's gravity well, the exponent in the rocket equation would be broken. This could make space travel much cheaper.
Water rich asteroids are potential sources of propellent. Water can be broken into hydrogen and oxygen, one of the better chemical bipropellents.
And, in fact, importing water rich asteroids is one of the first things Planetary Resources hopes to do.