On a small budget, I think it boils down to Rhino and Fusion 360. OnShape is in the running but last I checked it was quite a bit behind Fusion.
If you could tell us a bit more about what your company makes, it may help us to steer you in the right direction. The reality is that I wouldn’t consider any of those two options as viable in the long term as your main CAD for most businesses. I think you need to consider how you’ll transition out of that CAD software once you outgrow it.
Think of how long you’ll need to maintain parts. If you’re a company that’s building a “system” where you plan on heavily reusing parts between product. Think Ikea or Lego, where a lot of the products are reusing a lot of common parts, don’t even consider an introductory CAD. Cut you losses and get into something like Solidworks, Inventor, Creo… You’ll be kicking yourself in the pants when you need to transition a lot of parts to a new package. No matter what the sales guys will tell you, it won’t be seamless.
Other than some odd exceptions, I wouldn’t consider Rhino as your main CAD. It’s a great tool but I always see it as a Swiss army knife. It does a few things well but it doesn’t work as an overall long term solution. You can hack together a workflow to make just about anything with it. But it’ll always remain exactly that, a hack. It’s an explicit modeler so you’re directly modeling the surfaces. That makes it very quick a creating mockups. It also means that if you want to change say a fillet radius you’re basically stuck starting from scratch or several steps back. The quick mockup, possibility to create complex surfacing (difficult to learn mind you), Grasshopper computational design, ability to open just about any CAD file and fix things make it a great asset but it doesn’t make sense as your primary CAD beyond early design phases and in a few very specific cases.
Fusion 360 on the other hand, is built a bit more like the standard mechanical CAD packages. It’s missing some features and the cloud aspect can be a PITA. But it has some nice sculpting features and has most of the basic features you’d expect at this point. I’ve used it to build a few parts and it gets the job done.