Should I graduate to floor standers or will larger bookshelves suffice?

It is really hard to say what is the best general approach you should take, much less specific recommendations.  The larger cabinets of a floorstanding speaker suggests deeper and stronger bass response, but whether that is “better” is hard to hazard a guess.  I once heard a demonstration of two ProAc speakers—one a bookshelf speaker on a stand, the other a more expensive floorstanding speaker—both were good, but I preferred the smaller, cheaper, speaker.

As for subwoofers, I find them to be a bit tricky to properly integrate into a system, and I don’t like having to constantly fiddle with adjustment.  How deep must your bass go to be satisfying?  I think most people will be surprised about what constitutes great sounding bass.  I know a custom builder who makes systems that sell for as much as six figures.  He now uses 18” woofers that are made to his specifications.  They are designed to deliver a wide frequency range and a very fast and clear sound, which means very light cones and restricted excursion.  I hear what is great bass from these gigantic woofers and was surprised to find out that went down only to around 40 hz.

There is a middle ground between floor standers and bookshelf speakers.

Stand mounts they are called.

I own a pair of Reference3A DeCapo I "stand mounters".  Way too big for bookshelves, but half the height of floorstanders.  Surprisingly copious cabinet volume which of course helps the bass.  I think they are 10 or 12" midwoofers.

I tried Proac Floorstanders, they were magnificent but required too much power (this was before Class D and I am a Class A/Tube guy).

The DeCapos are 90/dbw and incredibly musical...

Bookshelves that are well made will thump just as well as many floorstanders. Genelec 8351B or Dynaudio Confidence/Contour lines, or ProAc. And if you really need the low end, which in modern city apartments is seldom missed on speakers like these, you can add subwoofers which add value to floorstanding too. Note that Genelecs are 3-way, as are Dutch & Dutch or Kii Three. 

If you have the space of a gigantic house to house floorstanding , sure. But the notion that you need that format for a "full range" sound is tediously passe. 

Good advice from @soix

Might check in with The Music Room, Ascend Audio or Zu Audio ... especially Ascend.  All have models in budget and have 30 day return policies.

Stand mounts are a good suggestion. Wharfedale, Mission  and others are offering throwback big baffle speakers that are selling at a wild pace…at Mid Fi prices. I love my Wharfedale 85th Anniversary Lintons, stand mounted with good cables and a speaker level output REL T-Series sub.