New efficient speakers - best way to keep noise floor down?

Much depends on the cartridge’s output, and how much gain is required to satisfy your SPL cravings, from there. I wrestled with low output MC carts(.25 - .3mV), for a while, with my phono stage set to 68db gain. When I’d turn up the juice, could hear the 60Hz, picked up by the arm/cart/wiring, between tracks(low level, but there / no noise is good noise). When I switched from 86db/2.83V to 93db/2.83V speakers, that was more pronounced. With a Soundsmith Aida(2.2mV), and the ability to reduce the phono stage’s gain, the noise at my typically high listening settings(master volume), is now virtually nil(with ear at speaker). BUT- don’t burn that bridge, ’til you come to it(relax). Given you’re using an MM cart and have no noise issues now, you’ll probably be alright. You’re going to need much less twist on your volume control, to get the same SPLs, with those new speakers. If you do have noise, be certain it’s only related to the phono input, before taking steps. High sensitivity speakers will reveal noise from any source in your component chain. Happy listening!

My speakers are 101db, why do you think about noise floor problem ?
Did you get the speakers or it is just in theory ?

It depends on your cartridge and cables, also the amp and phono stage.
I can’t remember any noise problem with my 101db (Zu Audio Druid) speakers unless it’s a cartridge with extremely low output (lower than 0.15 mV). All MM/MI are dead quiet on the home listening volume level.

I would recommend AT-ML150 OCC with Beryllium Cantilever and MicroLine stylus tip if you want the best for the bucks. Or the AT-ML170 if you want one of the best MM ever. Here is the article for you about some decent MM. Australian JLTi made amazing phono stage for MM/MC for very reasonable price, previous version without new PSU was exactly $750 new. 

I worry about the noise floor problem because in my demo the bg noise was noticeable (but still sounded bloody fantastic). However, even though their analog equipment was totally different than mine, I think they are of similar quality so I'm thinking I might need to plan ahead.

What is the rest of your system. The way the noise floor gets reduced is equipment with equipment that has low internal noise levels. A quiet phono stage is a good start, but you also want a preamp and amp with low noise levels.