We use the hypernetted chain theory - complemented in a few selected cases by Monte Carlo simulations to assess its accuracy - to study a model fluid composed by hard spheres surrounded by an attractive square-well, followed by a linearly decreasing repulsive ramp. The proposed competing interaction allows us to study individually the influence of all the defining parameters on the formation of aggregates out of the homogeneous fluid, as signalled by the development of a local peak at low wavevectors in the static structure factor. We document an accurate linear scaling of the temperature whereupon aggregates develop (at constant density) as a function of both the square-well width and the height of the repulsive barrier, over a wide range of such properties; a much drastic dependence is instead observed on the repulsion range, well described by an exponential increase. We show that typical correlation distances among aggregates, in early conditions for their development, fall approximately at a constant fraction of the width of the repulsive barrier. We analyse different possibilities in which attraction or repulsion prevails in the overall balance of microscopic interaction: we document, as expected, that for sufficiently weak repulsion barriers, or sufficiently large attractive wells, the structure factor shows a trend to increase in the limit of vanishing wavevectors, heralding a standard liquid-vapour phase separation at low temperatures. At the opposite end, the development of aggregates seems to be hardly favoured, for the present model, if attraction is completely neglected.