Bootstrap can result in a rather samey appearance for sites that use it, but the only people who give a tulip about that are graphic designers; a degree of familiarity is a good thing for real users, who are trying to actually get things done rather than marvel over the colours, fonts, and spacing. As long as the limitations it imposes don't interfere with your artistic vision, use it and save yourself a load of time.
Jquery is really quite easy to pick up, as it's just a bunch of library routines hiding browser differences. Given that you don't have to worry about older browser support you should go straight for the 2.x branch, which eliminates a lot of leftover cruft.
As far as particular UI components are concerned, there are an absolute shedload of free Jquery plugins, of varying quality: the good ones do tend to rise to the top, and aren't hard to find, as long as you don't always just download the first result in a Google search
Avoid Angular.js like the plague. Imagine somebody read the whole of Design Patterns and Patterns of Enterprise Application Architecture, understood less than 1% of them (but thought they understood it all), then read the documentation for the most over-engineered, bloated app framework ever created and understood less than 1% of that, then took the knowledge they'd acquired and misapplied it in the worst possible way to a context for which it was utterly unsuited: they'd produce Angular.js; except it's worse than that.
For going the SPA (single-page app) route, it's probably worth jumping in with Backbone.js. It can appear a little daunting at first sight, but it's solid underneath and gives you a lot of good stuff that you won't manage otherwise, life being too short (literally, in your case).
So to summarise:
Then just keep going until you're done; I'm sure you know how to do that bit
There are a lot of worthwhile Backbone tutorials out there, as well as a lot of crap ones. A good place to start is Jeremy Ashkenas's list, as he created Backbone.js so he's a pretty good judge of them
EDIT: oh, one more thing: don't get hung up on the back end. Remember, as far as a client running in a browser is concerned, everything on the server is just stuff accessed over HTTP. It has a URL, which can accept certain request methods (GET, POST, etc.), and maybe parameters (e.g. GET http://banana.example.com/bunches/?ripeness=medium to get a list of all bunches of bananas of medium ripeness), and which returns a status (e.g. 404 Not Found if there are no medium-ripe bunches, 200 OK if there are) and a response body (an HTML page saying "Yes, we have no medium-ripe bananas", a JSON response containing an array of bunch IDs). That's all the client knows, and all the client needs to know. It could be implemented in PHP, or Struts, or node.js, or you could have a bunch of North Koreans sitting at Teletypes sending back responses; it doesn't matter.
Jquery is really quite easy to pick up, as it's just a bunch of library routines hiding browser differences. Given that you don't have to worry about older browser support you should go straight for the 2.x branch, which eliminates a lot of leftover cruft.
As far as particular UI components are concerned, there are an absolute shedload of free Jquery plugins, of varying quality: the good ones do tend to rise to the top, and aren't hard to find, as long as you don't always just download the first result in a Google search

Avoid Angular.js like the plague. Imagine somebody read the whole of Design Patterns and Patterns of Enterprise Application Architecture, understood less than 1% of them (but thought they understood it all), then read the documentation for the most over-engineered, bloated app framework ever created and understood less than 1% of that, then took the knowledge they'd acquired and misapplied it in the worst possible way to a context for which it was utterly unsuited: they'd produce Angular.js; except it's worse than that.
For going the SPA (single-page app) route, it's probably worth jumping in with Backbone.js. It can appear a little daunting at first sight, but it's solid underneath and gives you a lot of good stuff that you won't manage otherwise, life being too short (literally, in your case).
So to summarise:
- Use Bootstrap to get your UI layout in place;
- Chuck Jquery 2.x in there;
- Identify suitable Jquery plugins for any particular widgets that aren't already in Bootstrap - you can, of course, limit yourself to components written specifically for Bootstrap, which will make integrating them easier;
- Chuck Backbone.js (and its one dependency, Underscore.js) in there;
- Start creating the Backbone Models and Views, and the Router that connects them to the back end via HTTP.
Then just keep going until you're done; I'm sure you know how to do that bit

There are a lot of worthwhile Backbone tutorials out there, as well as a lot of crap ones. A good place to start is Jeremy Ashkenas's list, as he created Backbone.js so he's a pretty good judge of them

EDIT: oh, one more thing: don't get hung up on the back end. Remember, as far as a client running in a browser is concerned, everything on the server is just stuff accessed over HTTP. It has a URL, which can accept certain request methods (GET, POST, etc.), and maybe parameters (e.g. GET http://banana.example.com/bunches/?ripeness=medium to get a list of all bunches of bananas of medium ripeness), and which returns a status (e.g. 404 Not Found if there are no medium-ripe bunches, 200 OK if there are) and a response body (an HTML page saying "Yes, we have no medium-ripe bananas", a JSON response containing an array of bunch IDs). That's all the client knows, and all the client needs to know. It could be implemented in PHP, or Struts, or node.js, or you could have a bunch of North Koreans sitting at Teletypes sending back responses; it doesn't matter.

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