> [...] for a mix of fun, profit and self development.
Assuming you actually enjoy programming, fun and self development will likely come rather naturally as you build and break, find problems and develop solutions. If you have people looking at your products, even if they're just friends, learning to listen to their problems and solve them will also take you far.
Profit, on the other hand, is more difficult because that has far less to do with technology than it does with marketing and business. You could know every language, paradigm, framework, API, methodology, whatever and you'll not make a dime unless people see value in what you're building. Thus, if you actually have a real profit motive consider spreading your time between learning web development and business development.
> [...] how valuable would a back-end education be (node/express or ruby on rails), even if I end up going the baas route?
Even if you go the BaaS route you'll likely need some degree of backend knowledge to either a) have the BaaS do the right thing in the first place or b) actually understand the limitations of your BaaS, why those may be, and effectively evaluate alternatives.
In most cases, a BaaS will provide you easier ways of doing things like creating your own APIs or performing database operations. But at some level - even if basic - you need to understand your own APIs and how you're storing/retrieving data. You don't need to go particularly deep on any given topic (plenty of time for that) but you should be comfortable being able to explain your front- and back-end architecture to a fellow web developer.
> My product ideas are run of the mill Reddit for dogs, news aggregator, to-do list app type stuff
These are great starter projects; don't get discouraged because they are "run of the mill" because - as a developer - the value of novelty lags behind the value of productivity. A mediocre implementation of a mediocre concept showcases more progress as a developer than an amazing concept that doesn't exist.