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I have a little experience in building various models, but I've never created anything like this, so just wondering if I can be pointed in the right direction.

I want to create (in python) a model which will generate text based on multiple inputs, varying from text input (vectorized) to timestamp and integer inputs.

For example, in the training data, the input might include:

eventType = ShotMade

shotType = 2

homeTeamScore = 2

awayTeamScore = 8

player = JR Smith

assist = George Hill

period = 1

and the output might be (possibly minus the hashtags):
JR Smith under the basket for 2! 8-4 CLE. #NBAonBTV #ThisIsWhyWePlay #PlayByPlayEveryDay #NBAFinals

or

JR Smith out here doing #WhateverItTakes to make Cavs fans forgive him. #NBAFinals

Where is the best place to look to get a good knowledge of how to do this?

Generally, text generators work by modeling the joint distribution of the text by its Bayesian forward decomposition

$
beginalign*
p(w_1, w_2, ..., w_n) &= p(w_1) * p(w_2|w_1) * p(w_3|w_2, w_1) * ... * p(w_n|w_i_i<n)\
&= prod_i=1^n p(w_i|w_k_k<i)\
endalign*
$

From a modeling perspective, this looks right up RNN's ally, where you can have a state holding information from $w_k_k<i$ to learn a representation of $w_i$

Now, in your specific case, you're interested in a conditional text-generator, so you are trying to model $p(w_1, w_2, ..., w_n | v_j_j)$, but this same tactic works.

$
beginalign*
p(w_1, w_2, ..., w_n| v_j_j) &= p(w_1|v_j_j) * p(w_2|w_1, v_j_j) * p(w_3|w_2, w_1, v_j_j) * ... * p(w_n|w_i_i<n, v_j_j)\
&= prod_i=1^n p(w_i|w_k_k<i, v_j_j)\
endalign*
$

So, in your RNN or forward-based model, you can use the exact same approach just additionally embed the conditional inputs you have and somehow infuse it into the model (in practice, I have seen this through attention, concatenation, or some other common approach).

My recommendation (depending on the computational power you have) is to take advantage of the recent fad of pre-trained language models. Specifically, ones trained on next word prediction will probably do the job best. A good example is gpt-2, and, if you check out their GitHub, their code is very readable and easy to adjust for adding conditional input in the ways I have described.