Here's some pictures of things I pick for wood processing. The marbles bolo machete is mostly there to show you how thin machetes tend to be compared to more dedicated wood processors like parangs and kukuris. But, for lighter wood, bolos do decently since they have a weight-forward design. I keep the main edge for lighter cutting and sharpened the back edge more obtuse for chopping wood with less worry of denting the edge, since machetes are also run very soft compared knives.
Depending on how much other stuff you need, I find the RTAK II balanced pretty well for some slashing work and it can baton really well. The BK9 is in a similar realm but the RTAK works for my hand better.
For pure wood chopping, the my parang heavy duku chandong or HI kukuri are what I would pick as they are thicker and split wood better. Both are also 5160 and heat treated to be used roughly for a long time. I like the myparang handle a lot.
The Ontario SP-5 is a great cheaper option, around $50. It's really close to performance of the RTAK II, IMO, and is a better value. I bought both at the same time since I'm in research mode for big knives. You could get the bolo machete and SP-5 and still be within your budget.
One disclaimer on some of these knives, like the RTAK II and SP-5, I re-profiled the edges as they came too thick for my tastes, even for choppers. If you don't want to do that, maybe a different option, like a BK9 or myparang, would be better.
The marbles machete is probably the only machete I've ever bought that had a useable edge right out of the packaging. They are made by imacasa/condor so the quality is very similar. The orange paint won't last long.
I included a swamp rat R9, which I really like too but they're not readily available and above your price range. The handle seems to either work for people or it doesn't and it works great for me. Better than I expected. It would stink as a machete, as is, but makes a nice camp knife and chopper. I'll strip the coating eventually. It's one of the newer additions.