You can do what I do - I use the Photos to import my pictures via a USB cable. No iCloud configured for Photos on the phone or the Mac.
Or, if you don’t want to use Photos as your organizer, you can, as @simon wrote, use Image Capture to download photos from the phone. From there, you can organize them using whatever app you prefer.
In either case, when you connect the phone to the Mac with a USB cable, you will see it appear in Photos and in Image Capture as a camera device. From there, it is easy to select the device and import pictures from it.
And if you have other kinds of cameras (e.g. DSLRs or Android phones), the process is the same. If the device (camera or phone) can be connected via USB and makes itself accessible as a storage device, it will import directly. Or you can remove the storage (typically an SD or micro-SD card these days) and connect it to the computer via an appropriate USB adapter (or plug it in directly if your Mac is a model with a built-in SD card slot).
I’ve been using Apple’s software (Photos today, and iPhoto before that) for a long time. It’s not perfect, but it works for me. And you don’t have to configure all the iCloud features if you don’t want to use them.
I know that professionals like Adobe Lightroom, but it is only available via a subscription, and you may not want to pay for it. Adobe Photoshop Elements (no subscription, but you need to buy a new license and upgrade every 3 year, which sucks) includes a photo organization app. I’ve never used it, so I can’t tell you if it’s any good.
One important thing to note: Modern iPhones, in their default configuration, take pictures in HEIC format, not JPEG. This isn’t a problem if you’re using Apple software, but some third-party picture organizer systems may not support it.
I don’t know if Image Capture can be configured to convert HEIC to JPEG as a part of the import process. If it doesn’t, and your software doesn’t support HEIC, and you don’t want to install software to do the conversion, you can configure you phone to take pictures in JPEG format. See Here's how to change HEIC images to JPEG on iPhone | Tom's Guide
This isn’t a bad approach, actually. You can configure Finder folders to display thumbnails of each image when in icon view. And the MacOS-bundled Preview app has no problem viewing and printing HEIC images. And you can make edits with whatever software you like.
Popular image-editing apps include (in no particular order):
- Adobe Photoshop. Only available via Creative Cloud subscription. $23/mo for PS only or $70/mo for a CC Pro subscription.
- Adobe Photoshop Elements. Should be good enough for non-professional use. $100. No subscription, but the license expires every 3 years.
- Graphic Converter. $40
- Pixelmator Pro. A lot of people like this as an alternative to Photoshop. Owned by Apple since February. $50.
- Photomator. Designed for photo manipulation more than generic image editing. Also owned by Apple since February. Free installation, but with an in-app-purchase subscription ($120 lifetime, $80 lifetime special-offer, $30 yearly, $8 monthly). I have no idea what, if anything, you can do with it without a subscription.