There isn't a single floor, because the minimum is set by the sponsor and by the securities exemption they're using to raise. Most private storage funds are sold to accredited investors under private placement rules, and the accreditation test itself is the real gate for many people rather than the stated minimum. Whether you qualify and how a given offering is structured is a question for a securities attorney, and the sponsor's own counsel works for them, not you.
On the numbers you're seeing: $250k to $1m is the common band for a fund raising institutional money, and the $100k feeder is exactly what it sounds like, an aggregator that pools smaller checks into one investor position. Feeders often carry their own fee layer on top of the fund's, so ask for the total load, not the fund's load.
The fee stack you listed is recognizable. Asset management fee, acquisition fee on purchase price, carried interest over a preferred return, and a property management fee paid to the sponsor's own operating arm. Storage is management-intensive relative to, say, net lease, so a facility-level management fee is normal. What matters is whether the sponsor's management company is charging market rate or a premium to itself.
One thing worth pinning down: whether the asset management fee is on committed capital or invested capital. On a fund that takes three years to deploy, that difference is real money paid on cash sitting in a bank account. Ask for a fee example on a hypothetical $500k commitment across the full fund life, expressed in dollars. Sponsors who won't produce that are telling you something.
