I had a $5 knife from Daiso, the balance was very nice, I really liked it. I bought it around 2008? A friend has it now, they like it. Cheap knives are rarely full tang and will rust inside the handle, I drip oil into the handle, dry them carefully, and they last for a long time.
My recommendation would be to get a cheap knife like that and a nice carbon steel cleaver like The Wok Shop, or your local Asian market sells. With those two and less than $20 outlay you can do most anything. Breaking down Winter Squash is a pain, but doable, or you can get something heavy and brutish just for that if it’s you thing.