Time series prediction where each datapoint has a sequence

I am Computer Science major, and new to stats, so please bear with me and point me to the right direction if what I'm asking is pretty obvious.

I have a dataset, where each data point consists of M features (e.g. name, age etc. both continuous and categorical - I might bin them or something and organize them properly) and a time series with data for times T1, T2, ..., Tn. The event dates are in months.

The time series can be a sequence of dates of joining new jobs, which means that the whole dataset describes job - changing characteristics for a few persons, each datapoint representing a single person.

I want to use machine learning to train a model with this data, and then given an exactly similar test dataset, I need to predict the time Tn if I'm given the sequence from T1, T2, ..., Tn-1. Something like that. So this isn't exactly the common time series prediction.

Another example can be shown with e-commerce datasets like: time series data of purchases for N items. For each item (on a single row) on the site we have the item's attributes, and a sequence of purchase timestamps with purchase quantities and purchased-by user IDs. I would need to analyse this and train a model such that if I'm given a certain item with its attributes and time series data, I can predict future purchases.

I'm confused about what tool I should use and how this thing can be used to build a model.

Linear regression? If yes, how? How does my data fit into it? HMMs? SVMs? ANNs? The problem seems very similar to future retweet time series prediction if we're given historical retweet data for a few tweets (in hour scale), where each datapoint represents a time series of retweets. But I can't seem to grasp my head around this. Any help will be really appreciated.