A lot of work has been done in designing mobile robots. Although a lot of solutions appeared it remains a challenging subject. First of all you have to choose between two types of mobile robots; holonome or non-holonome. Holonome mobile robots have the capability to move in any direction and their motion is smooth. However, you have to pay for the complexity of the design and even in the control law. On the other hand non-holonome robot are simple to design but the non-holonomy requires that you have to consider this constraint for the design of a robust control law, specially if you need to carry varying payloads.
It depends a lot on where you want your robot to move. Is it indoor? Outdoor on concrete? Or even on grass?
(An extreme case are robots engineered mainly to overcome obstacles in search&rescue scenarios - these robots look like tanks and can drive over many terrains including stairs and walls that have fallen down ... but I guess you want "wheels".)
I would say that holonomic robots are easier to control and design. In non-holonomic robots (e.g. cars) the robot has less freedom as it has an orientation and cannot rotate on the spot.
Omni-wheels can be a solution to realize a holonomic robot easily with fixed axes, but omniwheels do not work perfect on all underground and they rely on a certain amount of friction. (This friction varies between different floors and between dirtiness of floors, so if you rely too much on odometry it is bad.)
Putting each wheel on an axis that can be rotated could be a solution that is mechanically more complex and also more complex to control but the actuation can be more precise.
Another nice solution is to have two wheels in one axis and one rotating unactuated wheel in the front and back of the robot. This is not holonomic but could be sufficient for your purposes (the roombas work like this).
There are lots of mobile robots and good ones. Everything depends on the other criteria or constraints you have: energy consumption, size, shape, what are the other Devices the robot Will carry and especially sensors...
Maybe you should also care about the proximity of the provider for maintenance and upgrade issues...
For example In France Robosoft and Muse companies have very good wheeled robots (www.robosoft.com).
I suggest you use a cooperative redundant multiple steering system (CRMSS). The advantage of CRMSS is that if one steering system is about to fail it is backed up by the other system(s).
There are two ways of steering a wheeled vehicle. One is to steer one or more steerable wheels. The other is do drive one or more left hand wheels independently of one or more right hand wheels. If acting alone each system has a specific centre of curvature (COC). In a CRMSS all systems are enabled but have identical COCs.
In cars and traditional tractors conflict between the two steering systems is avoided by disabling the drive wheel speed steering system by incorporating a differential into the drive train to the driven wheels. In zero turn radius mowers the wheel angle steering system is disabled by making the non driven wheels into castors.
Such a single non redundant steering system is OK on flat ground, but on steep slopes stability, traction and manoeuvrability problems arise.
The above safety problems can be overcome to some extent by enabling both steering systems but allowing one system to overpower the other. In vehicles with locked differential(s) the wheel angle steering effect overpowers the drive wheel speed steering effect. Conversely in skid steer vehicles the drive wheel speed steering effect over powers the wheel angle steering effect. However this solution to the above safety problems introduces environmental problems. These are increased ground damage, tyre wear and fuel consumption.
However a Cooperative Redundant Multiple Steering System combines (or exceeds) the safety advantages of vehicles with conflicting redundant steering systems with the environmental advantages of a single non redundant steering system.
No one has mentioned a chassis that has motors on each of 4 wheels and is articulated in the middle. Its steered by bending at the center, slowing the inside wheels and possibly increasing the speed of the outside wheels. This chassis steers well under heavy daft loads an is used on very large farm tractors. Some call it crab steering now, but crab steer is when each individual wheel turns as it does on this IH 4300 forty four were made in the 60's by slightly modifying a Hough loader. Some parts didn't stand up to well to pulling a load 24 hours a day when the temperature got over 115 F. They steered we under load. Overhauling a dive train was very expensive.
Without knowing what task your robot will be required to perform and the surfaces it is preforming them on I can't be much help on wheels. If your on tilled soil you'll need large wide tires with aggressive traction for high clearance in rough ground or much smaller wheel are fine in clean warehouse.