You should read the wikipedia article on nuclear reactions for a start.
While the number of possible nuclear reactions is immense, there are several types which are more common, or otherwise notable. Some examples include:
Fusion reactions — two light nuclei join to form a heavier one, with additional particles (usually protons or neutrons) thrown off to conserve momentum.
Spallation — a nucleus is hit by a particle with sufficient energy and momentum to knock out several small fragments or, smash it into many fragments.
Induced gamma emission belongs to a class in which only photons were involved in creating and destroying states of nuclear excitation.
Alpha decay - Though driven by the same underlying forces as spontaneous fission, α decay is usually considered to be separate from the latter. The often-quoted idea that "nuclear reactions" are confined to induced processes is incorrect. "Radioactive decays" are a subgroup of "nuclear reactions" that are spontaneous rather than induced. For example, so-called "hot alpha particles" with unusually high energies may actually be produced in induced ternary fission, which is an induced nuclear reaction (contrasting with spontaneous fission). Such alphas occur from spontaneous ternary fission as well.
Neutron-induced nuclear fission reactions – a very heavy nucleus, spontaneously or after absorbing additional light particles (usually neutrons), splits into two or sometimes three pieces. This is an induced nuclear reaction. Spontaneous fission, which occurs without assistance of the neutron, is usually not considered a nuclear reaction. At most, it is not an induced nuclear reaction.
An intermediate energy projectile transfers energy or picks up or loses nucleons to the nucleus in a single quick (10−21 second) event. Energy and momentum transfer are relatively small. These are particularly useful in experimental nuclear physics, because the reaction mechanisms are often simple enough to calculate with sufficient accuracy to probe the structure of the target nucleus.
From this list one can see that "direct reactions" are specific scattering reactions with the purpose of studying a particular nucleus. Thus the former list of nuclear reactions cannot be described as a combination or a series of "direct reactions".