Buy now or risk the cheapest fares being sold out. A quick check shows that Super Economy Trenitalia tickets and Low Cost Italo tickets (Venice to Florence only) are still available for certain times on your travel dates. As you already seem to know, the cheapest fares come with restrictions and are often non-changeable and non-refundable. Italo sometimes has discounted fares available after Trenitalia's discounted fares are sold out, so explore that option if you decide to wait.
I always buy directly from the train companies, so I can't comment on the Trainline app. Some resellers (I believe Trainline is a reseller) sell trips that are partly on Trenitalia and partly on Italo, so be attentive as those trips may not be protected if the first train is late and you miss your connection.