The free county route is workable and it's where almost everyone starts. Two corrections to what you've been told, though.
Assessor records and recorder records do different jobs. The assessor holds the tax roll: parcel number, owner of record, tax mailing address, assessed value, and usually a rough building description. That's the file you want for outreach, and the tax mailing address is the single most useful field on it, because when it differs from the property address you're likely looking at an absentee or inherited situation. The recorder holds documents, deeds, mortgages, liens, and that's where you look later when you're checking whether the person you're talking to can actually sell.
On @halyard's point about sale prices: that depends entirely on your state. Roughly a dozen states are non-disclosure, meaning sale prices aren't part of the public record at all, so the parcel page will show ownership and assessment and no price history. Ownership is public everywhere. Price is not.
Many county GIS maps do let you click a parcel and get the number, which solves your search problem. If yours doesn't, the assessor office will usually answer the phone and tell you how their own site works.
Skip tracing sits after this step, not instead of it. You feed it a name and address to get phone numbers, so you need the county record first. And expect the tax roll to lag. Owner of record can be months behind an actual transfer, and a house that just sold to another investor will still show the old owner. Cross-check before you mail 60 cards.
