"Is TT Home & Business the right version for me?"
Yes, the Home & Business version should work just fine for your purposes. I would suggest that you read through Publication 535 (links below) with respect to business expenses.
Regarding your stated objective, you should be aware that hobbies/activities engaged in not-for-profit have limits on losses that can be deducted from other income.
See https://www.irs.gov/publications/p535#en_US_2018_publink1000208630
Regarding expenses incurred prior to "going live", those are start-up expenses of which you can deduct up to $5,000 and must amortize amounts in excess of that figure.
See https://www.irs.gov/publications/p535#en_US_2018_publink1000208919
