The 2PL model is the default model in the Item Analysis platform. The 1PL model is appropriate when you can assume that all items have equal discriminating power. When this assumption is not appropriate, the 2PL or 3PL model should be used. The 2PL model has greater numerical stability than the 3PL model, especially for small data sets. In addition, in the 2PL model, b can be interpreted as the ability level required for a 50% chance of a responder answering an item correctly.
The IRT model assumes that the underlying trait is unidimensional. That is, there is a single underlying latent construct. If there are several traits that have complex interactions with each other being measured, then a unidimensional model is not appropriate. The IRT model is appropriate for continuous latent variables. For a categorical latent variable, you should consider a latent class model. See Latent Class Analysis. IRT models are assumed to be item-invariant. Item-invariance means that P(θ) is interpreted as the probability of a correct response for a set of individuals with ability level θ. If a large group of individuals with equal ability levels answered the item, P(θ) predicts the proportion who would answer the item correctly. This implies that IRT models would have the same parameters regardless of the group of subjects tested. In addition, the IRT model assumes local independence, which means that once the latent construct has been accounted for, the items are independent of one another.