A single share of a listed data center REIT is real ownership of data center real estate. You hold a proportional interest in the whole portfolio, get your share of the dividend, and can sell it any day the market's open. You need no license and no insurance to own it, the same as any other stock. The private funds with $50,000 or $250,000 minimums are usually private placements, and the minimums exist largely because those offerings are limited to investors who meet accredited standards under securities rules, so whether you qualify is a question for a licensed professional.
On @juniper's question, the split is worth learning because it changes what you own. Hyperscale means very large facilities leased in whole or in big blocks to cloud providers and technology companies, often on 10 to 15 year leases. Colocation means a facility where many customers rent space and power in the same building, with shorter terms and more turnover, and retail colo is the small-cabinet end of that. The listed REITs do both, with different mixes, and the mix is disclosed in their filings. Private funds tend to concentrate on one.
The cost most beginners don't expect is information. Sector rent and vacancy data comes from paid research services that run from a few thousand dollars a year upward, well past what a small holder would spend. You don't need it. The REIT supplemental disclosures, published every quarter and free, carry megawatts leased, lease expirations and development pipeline detail, which is most of what you'd actually use.