Sam has a downer on 12" subs. I don't.
Nexo simply don't make bad kit and my 12" Yamaha sub (now Dave B's) was absolutely fine with the DXR10s.
You too will be fine provided you use the controller and a suitable power amp (if it's not one of the combined units). But you must make sure that both the DXR15 and the sub have the same low pass filter high pass filter and low pass filter frequencies. It looks like they are all adjustable on the NEXO controller, so make sure they are set to the same value as set on the DXR15s (either 120Hz or 100Hz - you'll need to see what works best for you).
15" FOH speakers are useful if you got a band and haven't got subs but have say keyboards, so you want a good low end to the speakers. You can put kick and bass through them if necessary to add a bit of extra low end. You may not have them very loud in a pub when there's no need to mic the drums or bass or guitars, but there's still that extra bit of low-end compared to 10" or 12" for keyboards. But you'll never get the low-end thump out of them that you'll get with a sub which that helps with the whole audience experience in a decent sized venue.
But you have spent more than you needed to on the DXR15s when with subs, the DXR10s or even DXR12s would be smaller and lighter and do the just same job as the DXR15s as they'd all use the same low pass frequency setting, so all would be handling the same amount of mid and high frequencies down to 100Hz or 120Hz.
With the subs you can at least now easily determine the volume of the low end
We did try and tell you not to pick the 15"s and use 10"s or 12"s instead, especially with subs. We know you'll have to carry them to and from gigs!
Where were you trying out the tops? At home or in a decent sized rehearsal space? Any small space or any large empty space can sound boomy with a lot of volume. A decent sized space full of punters should sort that out. Also, you need to understand what the sound is like in front of the speakers, where the audience will be. Standing behind them you get a lot of bass radiating from the rear of the speaker (it's the way bass projection works), so they will sound more boomy to you than when out front.
It's worth trying setting the high pass filter switch to first 100Hz and then 120Hz to see how much low end and boom you loose. That's what will be filled in by the subs at a volume you decide.
Your problem with a desk is that from what I understand, you only really need a single mic input (although if that's a radio mic then you'll need a line input) and a stereo line input for the backing tracks. So that says 'small 'desk', but really you need the facilities of a bigger desk.
You'll probably want some built in FX to provide a basic reverb for your voice.
You really need one pre-fader aux. channel for a monitor.
If you move to an external FX unit, then you'll need a separate post-fader aux. channel for that, and it's normally best to have that coming back on another stereo channel as this gives you the ability to EQ the effects, which using a stereo effect return doesn't.
You'll certainly want EQ, but this is where it gets tricky. You are seemingly doing this professionally (or at least semi-professionally) so you need to view it in a professional light. Not all EQs are the same. Fixed EQs all have different centre or shelf frequencies. But far more useful are swept EQ controls. One swept mid EQ is good. Two swept mid EQs are better. An sweepable bass EQ control is also good.
But to get all that on one channel means buying a physically large analogue mixer, or else a much smaller digital one. I'm not an expert here, but you should be able to get a much more comprehensive EQ per channel, plus built in programmable effects (so you don't need external effects), graphic EQs to balance the FOH sound (and knock back any bass frequencies that may still cause problems).
QSC Touchmix 8 say? I know it's very expensive new for an 8 channel mixer, though used is now an option as they've been out a while, but it really is a good little digital mixer. You can also use it to record your performances for reference and self-improvement. Sam, thoughts on other cheaper but equally useful digital options?