Short answer
Decide how much history you really need to move, name an owner for each data set, and start cleaning vendor, employee, chart of accounts and asset records well before implementation begins. Then rehearse the conversion more than once, so that reconciliation is routine by the time you go live.
Data is where a lot of good ERP projects lose time, and in my experience it is almost never because the new system cannot accept the data, but because nobody on the agency side owns the decisions about what to keep, what to fix and what to leave behind. I would start by agreeing on how many years of transactional history you need in the new system and which older records can live in an archive or a reporting database, since moving everything is expensive and rarely necessary.
Next, give each major data set a named owner, like your AP manager for vendor records and your HR lead for employee records, and have them start cleaning now by removing duplicates, closing inactive vendors, fixing addresses and settling on naming rules. The chart of accounts deserves its own conversation, because a new ERP is the best chance you will get to simplify it, and the redesign will go much better if finance has agreed on the new structure before the implementation partner asks.
Finally, plan for at least a few mock conversions, each followed by a reconciliation that your own staff sign off on, so that problems surface in a test environment rather than on your first payroll. If you want a starting point, the Start at Zero Navigator includes a data readiness section, and it is free.