An anaphoric relation can be either direct or indirect. In some cases, the antecedent being referred to lies outside of the discourse its anaphor belongs to. Therefore, an anaphora resolution model needs to consider the following two decisions in parallel: antecedent selection—selecting the antecedent itself, and anaphora type classification— classifying an anaphor into direct anaphora, indirect anaphora or exophora. However, there are non-trivial issues for taking these decisions into account in anaphora resolution models since the anaphora type classification has received little attention in the literature. In this paper, we address three non-trivial issues: (i) how the antecedent selection model should be designed, (ii) what information helps with anaphora type classification, (iii) how the antecedent selection and anaphora type classification should be carried out, taking Japanese as our target language. Our findings are: first, an antecedent selection model should be trained separately for each anaphora type using the information useful for identifying its antecedent. Second, the best candidate antecedent selected by an antecedent selection model provides contextual information useful for anaphora type classification. Finally, the antecedent selection should be carried out before anaphora type classification.