Both legal numbers you heard are real, for different jobs. Having counsel review an operator's form operating agreement and give you a memo on what it does to you runs roughly $3k to $8k. Negotiating a genuine two party JV agreement with bargained consent rights, a custom waterfall and funding default remedies, with markups going back and forth, is more like $15k to $40k on your side, and the second and third rounds of markups are where the meter runs. Some deals split the cost. Ask early.
Operator diligence is cheaper than people expect. Background and civil litigation searches through a vendor run a few hundred to about $1,500 per principal, credit checks need written consent, and reference calls cost nothing but time. Property level reports get paid out of the deal.
On size, the line isn't fixed. Small operators buying a $1.5M building will absolutely take $250k as the equity side and negotiate with you. Institutional style JV equity checks tend to start in the low millions. What varies is whether you're the only outside money, because that's what gives you something to negotiate with. If four other people are writing $250k for the same deal, you're a limited partner and the paper will say so.
One thing about that math: $20k of legal fees against a $250k check is 8% of your capital before you own anything. That ratio is the real reason small checks tend to end up on standard documents. If you go the small route, spend on reviewing the doc rather than rewriting it, and put the savings into checking the operator. And if you ever pool anyone else's money alongside yours, that's a securities question for a lawyer before you take the first dollar.