Hi, Thanks for the detailed requirements....
Definitely understand where you are coming from and what your needs are. Here are my thoughts on your options with some reasoning laid out.
Your budget does NOT allow for a professional install. For a professional install, the cost of labor is the killer. Think of how long that would take you to pull the wire to the top of your house and drop it into the exterior locations, now pay a company to do that. On the cheap side, this is at minimum 4-7 hours per camera, so take an hourly rate and start doing the math and you will find at 5 or so cameras, it starts getting pricey per camera as rates for installers run on low end $60 PER HOUR to the high end, $150 PER HOUR. The installers have a lot of overhead in the security industry, so just respect the fact that camera installations range from $500 to $1200 PER CAMERA... this does not include the cameras / hardware.
With that out of the way, a system that immediately meets your expectations is a hardwired setup. Expect to pay south of $1000 for an entry level consumer kit. Look at the PoE camera kits from Amcrest or Reolink. Go with the 4K camera kits, 8 channel. They sometimes come with 2tb hard drives, you would want a minimum of 4tb to get 30 days of continuous recording (1tb per 4K camera)... should be able to replace that 2tb hard drive or find the kit on their site without the hard drive. For hard drives, use Western Digital Purple or Seagate SkyHawk... both surveillance rated drives. Very common to need to go back in time 3 weeks ago to review footage. Also, don’t forget the Cat5E cable. The kit I’m referencing below has (4) 60 foot cat5e cables. If you prefer to run your own cables and need longer, Monoprice brand is a good quality cable... but you will need to put the ends on. Otherwise, purchase pre-made patch cables at the lengths you need if the 60 foot ones are not enough. I find it easier to make the cables though with a pull-through crimper. Don’t go outside brands of Amcrest or Reolink... you will be tempted but these are pretty much the gold standard and you can get support from them. These are white labeled Chinese product but they are established brands in the USA. Much of the other cheap camera brands are going to be one-off shops that have little community support with no engineering resources behind them for future support, etc...