Nothing wrong with BYD, it's a well made unit, they make the batteries that go in EVs, and the nice thing is that is a stacking system, so you can add further batteries units with little hassle. I'm not a fan of Chinese products, so I wouldn't recommend these unless I though it was worth it, they are also usually sold with SMA controller,, which is the important bit. However as space isn't an issue, I would go with LG units. Your hob is very unlikey to be taking full whack at any one time, and discharging batteries quickly doesn't do them a lot of good.
As you are working from home, then a larger PV array makes sense, your base level loadings will be relatively high - PC, printer, lights, modems etc etc all add up to a reasonable load of, at a guess about 0.5/1 kW. So a larger array will cover that base laod even in winter and possibly on a rainy day. Given that you are in North Wales, famous for mountains by the sea ( my granny used to live in Colwyn Bay), you no doubt get a lot of cloud cover, again a larger array helps. It also has to be said once you start fitting solar, the cost of making the array bigger isn't that high, the expensive bit is the base cost of doing any installation. I've just had a quick look at inverters SMA do a 5kW sungle phase unit that will take upto 7.5kW of panels £960, and Solaredge have released a 6Kw single phase unit that will take upto 9kW of panels £960 + the optimisers. Solis do a 6kW unit that takes 6.6kW of panels at around £500. Prives inclusive of VAT. If you do go down the Solaredge route, I woud suggest buying panels with the optimisers built in, this halves the number of cable joins behind the panels, and chances for a duff joint to cuase trouble with water ingress.
Incidentally, with the demise of the FiT rates, registering a system with MCS is now pointless, the only people you need to talk to is your local DNO - I would do this before parting with money as they may not approve a system over the nominal 3.68 kW (that's the inverter) they have to allow. I would also check your grid voltage, if this is floating high towards the max 253V allowed on the national grid, it may prevent the system form working properly. Again the DNO should be able to reduce this, but only they can do that.