Not sure how knowledgeable you are about external drives and not trying to insult you by my response.
Reasonably priced and wireless drive really don't go together. I would not go with anything less than Apple's 2TB Airport Time Capsule $299US. But if you're going to spend that kind of money you may as well go with a NAS. A NAS gives you a lot more features and you can find a really good one like a QNAP 2 Bay with 2x4TB drives for around $500. Believe me the extra money is worth the added security of your backups if you run the two drives in a RAID 1 configuration. Which means that one drive mirrors the other drive. So if one fails you don't lose all your data.
I would be more concerned with dependability over price. I have two wired external drives and a NAS for my backups. The reason I have wired backups as well is so I can clone my iMac drive and use it as if it were my internal drive should the internal drive in my iMac fail. Seriously think dependability. Reasonably priced drives fail. I have seen it many times and have had the experience once myself. Hope I didn't insult you and my info will help you. Thanks.
Not insulted in the least and appreciate the info. I’m really not sure I even need a back up. I don’t really store anything important on computer. Music is Apple Music, pictures are all on Amazon Prime photos and I don’t really store any important documents on the computer either.
Then why not just use iCloud. Probably the cheapest approach. For $0.99/mth you get 50GB storage. iCloud price tiers are pretty reasonable.
I do currently do that exact suggestion. Just didn’t know if I needed something for the computer operating system.
If you were worried about the OS I suggest using Carbon Copy Cloner. The program will make an exact clone of your drive which can be used in case of failure of your internal drive. It can be cloned to any cheaper external drive. A cloud backup will not copy your OS or programs. It only copies your data. You can use CCC for free for 30 days and see if you like it.
You're welcome and a Happy New Year to you.