You're coming over at a good time, the weather is definitely starting to get better.

Important hiking kit includes waterproof coat and overtrousers, sensible footwear (imo walking boots), a bag, and sufficient layers, but you can get easily get away with cheaper/less-technical layers and waterproof overtrousers provided you use common sense. Also bring a map, compass, phone, head torch, and basic first aid kit.

If you like mountains like myself, you should know that the further north and west you go, the hillier it gets, with our mountains being found in Snowdonia, the Lake District and the Scottish Highlands. Moorland and hill areas are more common, and these can make for good easy walking depending on terrain. We also have an abundance of coastal paths.

May and June are my favourite seasons for hiking as they are the driest, with some spring colours, and before the heat of the summer sets in (and the tourists).

I don't know where you're moving to, but the wetter areas are to the west of our hills and mountains, whilst the east is generally drier. Coastal areas will be warmer in winter and cooler in the summrr relative to inland areas, and of course it is colder up north in general.

My personal favourite hiking regions are Southern Snowdonia, the Cairngorms, and the northern half of the Lake District, but you can find decent places to walk anywhere.