Some of the items you are sewing have lots of layers, and many machines won't handle that well. My Janome won't, and I've loaned my Bernina to owners of both Pfaff and Brother who couldn't get through with theirs, either.
Yesterday I finished a hooded baby towel for the new grandson of a good friend. It's a free pattern from Shannon terry. I modified the pattern as I wanted to used a heavy flannel from Timeless Treasures rather than the Cuddle. So - hood was terry w/ flannel, bound across edge with double fold flannel. That's 6 layers right there. That was sewn into the edge of the towel - another layer each of terry and flannel for the body of the towel. Finished with double fold binding. At the juncture of the hood/hood binding/towel/binding there are 12, yes 12 layers. Two terry and 8 flannel. Bernina handled it without a hiccup.
So - while I wouldn't go with the low end Bernettes - I'd recommend a Bernina. Yes, it's going to be a stretch, and you won't be able to get a new one in your price range, but I'd be looking for a good dealer who sells used machines.