New Ubiquiti WiFi Setup

Hi Everyone

First off, just want to say these forums have been a massive help in helping getting us setup here in NZ after recently arriving from Europe, has been a hell of ride but the info and advice given here has really made some of the decision easier.

So my question/issue is related to our home network setup. I use to run multiple Apple Airport's to get our home WiFi network going; which was OK but not the best in terms of speed, so wanted to go it 'right' with some new equipment here.

We have recently moved into a new house that has ethernet already in the wall, and had the fibre installed on the weekend and are using a Huawei HG659 in the lounge that we got off TradeMe just to get us started as I would need something that can handle alot of connected devices.

Originally I was thinking of getting a Ubiquiti UniFi Security Gateway Router and connecting this with the 'fibre box' in the garage and then having a UniFi Nano HD access point in the kitchen connected to a wall ethernet port to beam the WiFi through the house, and potentially added another one if neededIn the lounge there is one Ethernet wall port and as I have four devices that I would like to connect via Ethernet, I was thinking of getting a basic gigabit network switch.

I have a OK understanding of networking but looking for something that is easy to manage and setup, which is why I was thinking the Ubiquiti range due to the UniFi Controller software

So my questions are:

With the network switch in the lounge, could I use an 'unmanaged' switch or something a bit smarter? I am thinking either this one (https://www.pbtech.co.nz/product/SWHTPL1007/TP-Link-TL-SG1005D-5-Port-Gigabit-Unmanaged-Switch) or this (https://www.pbtech.co.nz/product/SWHTPL1002/TP-Link-TL-SG105E-5-Port-Gigabit-Easy-Smart-Switch)

When I look at the networking box in the garage, would I be right in thinking that I could get away with not having a router at all? and simple connecting with ethernet cables straight from the white box where the fibre is connected and straight into the network 'distributor', or do I need this router to setup the access point (see pics)

Any ideas would be appreciated.