but quite frankly have no idea where to startPick up their respective SDKs, read their docs, and spruce up on their primary languages (Objective C for iOS, Java for Android). Having a device for each will be needed in the long run, but you can get started with just the SDKs and emulators.
If I choose a platform now (iOS or Android), am I essentially "stuck" in the platform or can I jump between the two?
Not really, but as mentioned above, you will be jumping languages in most cases. If you're planning on supporting both platforms (or more), standardizing your back-end and any intermediary code/technology will save time and effort.
What do I need in terms of knowledge, skills, funds(?), to begin this learning process?
Funds will be specific to your venture, but a good foundation in C++/Java is more than enough to get you started. Get reading!