For wiring:
I would do UCG 2.5GbE port -> USW 2.5GbE port > UAP 2.5GbE. Your Gateway and Switch have 10GbE ports and it may look like the better connection between them, but this may be valid only if you have >2.3Gbps ISP service and for aggregate traffic to multiple USW wired clients and/or wireless through UAPs. Cameras - wired to any available PoE port, they don't need higher than FE throughput. Your USW-Flex-2.5G-8-PoE - note the power adapter for listed in specifications 196W PoE budget is not included. It's in Accessories section, model UACC-Adapter-AC-210W ($79). Get UPS for power backup. Not necessarily from Ubiquiti, but they have options in Integrations section (from $159).
For mounting:
Since none of your equipment was designed for rack mounting - any rack with shelves. I'm reusing the same one for few hardware changes already. If you really insist on all Ubiquiti branded gear - they have good quality racks, shelves, mounting brackets, etc. in Accessories section, but in reality may do exactly the same as non-branded cheaper options from Amazon.