How much to put down on your primary residence vs rental property

[Takahito Torimoto]

I apologize if this is such a basic question (starting to learn) but - I have some bookmarks I plan on reviewing (which landed me here) that talks about how to calculate whether a property is good as a real estate investment (rental property) - including how much you should put down towards the down payment.

But - how does that thinking compare/differ with your own primary residence?  No income would come "from" it, obviously - so does it make sense to do a shorter mortgage term (15 years) and/or put down a (very) high down payment?   Part of that question is also being able to compare that versus, using the difference (especially in the down payment) towards a rental property instead.

I ask because - I'll be coming up to needing to understand which makes more sense - whether to put money towards a (potential) new primary residence, or to use money towards a (new) rental property.

From a very quick glance, it'd seem to make sense to put it towards the rental property since it would (most likely) give me a better return than a lower mortgage payment (and less interest paid) on my primary residence.  But I'm wondering where the decision making is done to choose to put money towards one versus another?

I hope this made sense :-)