Firstly, welcome. I am sure folks on here will give you the benefit of their experience but a really good forum with a lot of knowledgeable and helpful folk is on MoneySavingExpert -
Green & Ethical MoneySaving — MoneySavingExpert Forum.
The general rule is, go as large as you can with your panels, i.e. max out on kWp as the price of panels is small compared to the overheads of installing. If you go over 3.68kW theoretical exportable generation then you need permission from your District Network Operator (DNO). The look at what impact your system may have on them balancing the grid and authorisation will depend, among other things, on how many other houses in the locality have PV. My application cost about £150 from memory, though others have said it was free and some have been quoted eye-watering amounts. It is also possible they the DNO will say you can do it if this or that infrastructure work is done (probably at your cost). So exploring that at an early stage would be worthwhile.
E/W-facing is quite good as you will get max production from the East array until about midday and then the same from the West array after that. You may not get the max output that you would see from a south-facing system but you will generate worthwhile and therefore usable amounts for many more hours each day. For instance, my WSW-facing array (3500Wp) generated peanuts (200W) all morning. As soon as the sun pokes its head past due south it shoots up to max production (3000W or so) within 30 minutes. Having spent hours plotting the path of the chimney shadow (on south end of roof) before installing I realised after install that a shadow cast over panels generating on 200W makes no real difference. This lack of morning generation annoyed me so much that I put my hand in my pocket and splashed out for a second array on my SSE roof. Not the cheapest way of doing things but now I generate usable amounts (1kW+) from early morning right through to an hour or so before sunset.
Another option would be to put, say, 4kWp on each roof but then have an inverter capped at 3.68kW. This should avoid the need to get DNO approval as you can never export more than 3.68kW. You may lose a small amount of generation around midday when both arrays are getting sun from the south but a small price to pay and overall you would be pushing the inverter for longer periods at its rated output which is supposed to be better than having a, say, 5kWp inverter pottering along with 3kW for most of the time.
You should look closely at any shading from those trees, not only at midday but late afternoon and at all times during the winter months. On my second array I have a shadow from that darn chimney. It hits at about 2pm in the summer and with 5% of one panel covered I lose 90% of production. This is costing me about 3kWh per day on sunny April to October days and smaller amounts for the rest of the year. Assuming that is only 100 days a year, that is 300kWh. At my feed-in-tariff that is £60. Trouble is it would cost about £1000 to rectify with other technology, so I cannot justify the outlay. If you do have shading issues make sure you use something like a SolarEdge system or the equivalent from SMA (can't recall what they call theirs). It will be more expensive but worth the expense. In this regard, so not listen to any installer who says that their model shows only 5% shade or whatever. you need to see when and how the individual panels are in shade and whether that is at a time the array as a whole is in direct, rather than borrowed, sunlight.
I don't know enough about built-in panels but from the aesthetics perspective they have to be a winner. Another technology that was new when I installed was PV/thermal panels. The front was PV but there was integrated thermal pipes at the rear. The idea was that the thermal soaked up some of the heat produced by the panels, thus cooling them and making them more efficient and giving free hot water in the process. I have no idea whether that product ever took off.
If you have a good old immersion heater tank (or would consider installing one as a heat store) then I would suggest looking at the Eddi from
myenergi.com. This is in IMO the best of the solar diverters. These things are just clever switches wired into the immersion heater circuit anywhere between distribution board and immersion heater. A CT clamp on the live incoming wire senses whether you are importing or exporting electricity. If you are exporting it proportionately gives the excess to the immersion heater. Actually, it can output to any purely resistive load like electric underfloor heating or oil-filled radiators. You'll see a lot of discussion on payback but based on my records I know that my device (an immerSUN) saves me between £80 and £100 per year on my gas bill and that equates to using electricity prices as the cost per unit in the data recording. I think this is because I have 22m of uninsulated pipe between boiler and tank, so heat losses in that mean using my GCH for heating water-only is inefficient.
myenerie also produce EV chargers - the zappi - and this can work in tandem with their Eddi. Have a look at their site.
HTH and keep asking those questions before you commit £ thousands to an install.