What is the best air conditioner for renters?

Yes, but the practical answer depends on the type. A portable monobloc needs no installation and no permission, so it is the realistic option for most renters: you only need a window to run the hose. A window unit is usually fine too, though your lease may set conditions and a support bracket is often required. A split or multi-split drills through the wall and adds an outdoor unit, so it requires written landlord permission, an EPA Section 608 certified technician to handle the refrigerant, and often an agreement about whether it stays or is removed when you leave. For short tenancies, a portable or a window unit is usually the sensible choice.

For a portable monobloc or most window units, no: you can use them yourself with no permit. For a split or multi-split, often yes. The outdoor unit and the wall penetration are a structural change, so a homeowners' or condo association usually has to approve it, and many US municipalities require a local mechanical or electrical permit for the outdoor unit and its dedicated circuit. Check with your building and your city or county before you buy hardware you may not be allowed to mount.

For a split or multi-split, yes. There is no US law banning DIY installation as such, but under EPA Section 608 only a certified technician may open the refrigerant circuit, and the EPA states plainly that this includes connecting or disconnecting the pre-charged line sets sold with “DIY” mini-split kits. That is worth knowing, because it is the opposite of how those kits are usually marketed. Doing the refrigerant work yourself voids the manufacturer warranty and risks a dangerous, illegal release. A portable monobloc, and most window units, need no installer at all: they are factory-sealed, so you set the unit down or fit it in the window and run the exhaust yourself.

A real air conditioner has a refrigerant compressor and can lower a closed room below the outdoor temperature, and it is rated in kW or BTU of cooling power. A fan only moves air and removes no heat. An evaporative 'air cooler' blows air over water, adds humidity, needs a window open, and cannot reach a set temperature. compare.ac lists only units with a genuine refrigeration cycle, so everything you see here is a real AC.