Both descriptions are describing different stages, so here's the split.
The absolute minimum to do one deal is your earnest money deposit plus whatever you spend confirming the property is what you think it is. Earnest money on a wholesale purchase agreement is often small, a few hundred to a couple thousand depending on what the seller accepts, and you should be able to get it back if you cancel inside your due diligence period. Add a title search if you order one, commonly a couple hundred dollars, and mileage. So a first attempt can genuinely be under a thousand dollars, and that's why people say phone only.
The recurring costs show up when you're trying to do this repeatedly. A CRM to track buyers and sellers runs roughly $50 to $150 a month at the low end. Skip tracing, meaning looking up phone numbers for property owners, is usually priced per record, often somewhere between 10 and 25 cents. Property data subscriptions vary widely, and phone service or dialers add more. Direct mail is the big one, printing and postage commonly landing around 50 to 80 cents a piece, so a 2,000-piece campaign is over a thousand dollars before you talk to anyone. Prices move, so check current rates directly with any provider.
What I'd set aside is enough to survive several cancelled deals in a row, because that will happen. If your deposit is $1,000, four dead attempts is $4,000 in tied-up or spent money before a single assignment fee arrives.
One thing that isn't a cost but is a requirement: an attorney or title company in your state who'll handle an assignment. Some won't. Find that out before you go looking for property, not after you have a signed contract.
