We report results from 12 simulations of the collapse of a molecular cloud core to form one or more protostars, comprising three field strengths (mass-to-flux ratios, μ, of 5, 10 and 20) and four field geometries (with values of the angle between the field and rotation axes, ϑ, of 0°, 20°, 45° and 90°), using a smoothed particle magnetohydrodynamics method. We find that the values of both parameters have a strong effect on the resultant protostellar system and outflows. This ranges from the formation of binary systems when μ = 20 to strikingly differing outflow structures for differing values of ϑ, in particular highly suppressed outflows when ϑ = 90°. Misaligned magnetic fields can also produce warped pseudo-discs where the outer regions align perpendicular to the magnetic field but the innermost region re-orientates to be perpendicular to the rotation axis. We follow the collapse to sizes comparable to those of first cores and find that none of the outflow speeds exceed 8 km s−1. These results may place constraints on both observed protostellar outflows and also on which molecular cloud cores may eventually form either single stars or binaries: a sufficiently weak magnetic field may allow for disc fragmentation, whilst conversely the greater angular momentum transport of a strong field may inhibit disc fragmentation.