Should I invest in solar PV panels, a home energy storage battery... or both?

As we were ‘fitting’ into the FIT scheme at the time, our arrays are 3.75kw split east and west which actually gives a good spread through the day. It is a Enfinity system but I didn’t have a remote monitor at the time. 
We added 4 modular batteries with a separate (add on) inverter (LuxPower) giving 9.6kw of storage but expandable. 
There were several problems with the battery installation as the clamps were chopped and reconnected against the manufacturers advice. This gave interference until I remade the connections which shows in bad feedback to the controller (now sorted) making the connection sum jittery. 
My latest discovery is to restrict the switching at low battery levels otherwise there is more chance of feeding back to the grid as power switches on/off in the house. 
All very interesting and useful!

What do you think about vertically mounted panels ? We have an unshaded south west facing gable end which gets the full force of the winter sun. It seems a shame not to use it. Our south east facing roof would be the main site for panels but the north west side is unsuitable.

Panels perform best when they're perpendicular to the sunlight. The further away from that you are the less they produce. Our roof isn't very steep so production is good in summer, when the sun is high, but drops off a lot in winter when the sun is low. A steeper roof would be worse in summer but better in winter.

If you have vertical panels they're never perpendicular to the sunlight so you'll never get maximum output. But they could do quite well in winter with a low sun.

Winter is the time we’d need more output for the heat pump - sounds like it’s worth considering.

You could mount the panels on angled brackets @juliamc if there’s enough room - that might help

I think the name of game is to use solar to charge battery with over night imports form grid if needed. Was with Ovo's EV everywhere but have switched to 4 hours at £0.075 kWh. You do need a large battery for winter when low solar. The round trip with Tesla battery is 10% loss. 

Incidentally @M.isterW over the time we’ve had our system, I would now say that solar PV pays back quicker and more effectively than battery storage although the option to charge off peak is obviously a game changer with battery added. 
I think I saw earlier or on another thread something about the losses or efficiency of converting solar to battery and then use which is why I’d recommend solar before battery. 
It’s also why I still hesitate to move my peak use without an off peak incentive although I will look very carefully once our current contract ends

I’ve been pondering this question - with a heat pump the winter electricity use goes up hugely just when the solar output would be at its worst. But charging a battery during off peak times relies on the tariffs being available. If the battery didn’t last the whole day then peak time costs could be astronomical. Probably the best thing to spend on would be more insulation.

Agreed - insulation (cavity wall, loft etc), draft proofing is key. You can get battery storage to last a whole day but what isn’t said a lot is the peak output level that you can get - do it’s important to factor that in as well otherwise you might still use power at peak times.