It sounds like RhinoCAM would be a good choice for what you have in mind, since you seem to get along with Rhino. This would give you full 3D capabilities that you could use with your 3-axis machine as well as strong 2.5D functionality. If you have a lot of legacy Inventor files, getting the 7-day license for Inventor Import would probably make sense, so you could store them all as Rhino native 3DM files: Download Inventor Import for Rhino - Buy Inventor file import plug-in for Rhinoceros Once you had them open in Rhino, the RhinoCAM plugin would do all the CAM work from there, within the same workspace.
Rhino plusRhinoCAM Standard would be at the top end of your stated budget at list price, and at the low end if you got it from us. If you decided you needed re-machining or 4th axis capabilities, you can always upgrade to a higher version.