Before changing anything, map what you have. Most contractors run a mix: a PM tool, an accounting system, spreadsheets for WIP and pay apps, a separate tool for timecards, email for approvals. Some of it is connected, much of it is not.
The useful questions are about flow, not features. When a change event is logged in the field, how long until accounting sees it? Is the WIP built from live numbers or retyped each month? Can you trace a number on the owner report back to the source record? Who approves what, and where is that approval recorded?
Scoring each area makes priorities visible. The weakest link is usually where month-end time goes, and where errors in the earlier tracks (missed sub change orders, stale cost-to-complete, unbilled changes) come from.
Fix the biggest gap first. You do not need to replace everything to get value; you need the numbers that drive WIP, billing and cash to stop being re-keyed.