The key is to understand the accounting treatment, where unrealized gains/losses go, and how to do reclassification adjustments for AFS. You should go over the treatment if classification is changed (i.e. HTM to AFS), but that's not as important as what I mentioned in the first sentence. It's really quite simple to summarize:
Debt: Trading, AFS, HTM
Equity: Trading, AFS
Trading: Record at Cost, adjust at FMV… all unrealized gains and losses and realized gains and losses go to N.I.
AFS: Record at Cost, adjust at FMV… unrealized gains/losses to OCI; realized gains and losses to N.I., and you have to reclassify any previous unrealized gains/losses when disposed.
HTM: Record at Cost, adjust using Amortized Cost… no unrealized gains/losses; realized gains and losses to N.I.
If a company selects the FV option, all unrealized gains/losses and realized gains/losses are included in Net Income irrespective of classification.
Beyond all this, I would highly recommend spending sufficient time with the equity method for significant influence.