I'm glad you're enjoying your gardening - it's wonderful growing your own veg and fruit.
First point, onions etc: If onions are grown too damp then they won't store. I have taken to growing mine inside my polytunnel to keep the summer wet off them. They also hate being surrounded by weeds. Ideally, onions need a hot dry time to ripen before storage - can be hard to achieve in Scotland. There is some effect from the variety you grow too, some naturally storing better than others.
I keep looking for tips on how to store my veg over the winter, but most of them require a 'frost-free' garage
- what's one of those? Nothing matching that description in this part of Scotland. We have a number of sheds and stone buildings, but none is frost-free when it's really cold.
Different veg require a variety of storage conditions. For me the most surprising is squashes, which I now keep in a cool room indoors - the hall in fact, and they keep fine well into the new year.
Carrots I now grow inside my polytunnel, both to make it easier to keep them weed free and to keep them out of range of carrot root fly. I find they keep well if left in the ground, which I leave very dry. I wondered about covering them with straw but I'm sure the mice I seem to share my polytunnel with would simply be attracted by that.
Potatoes are always a problem to store for me, as these are the produce most usually meant to be stored in the mythical frost-free garage. I tend to leave them in the ground and accept there will be some frost and slug damage. One year I found a mouse nest inside a large dug-out potato! The first year we were here I built a straw bale container for them, a sort of indoor clamp - it kept them frost free but the mice got in and I also found it too much of a bother to dismantle the bales every time I needed some spuds.
I do freeze some veg, such as peas and beans, also cherry tomatoes which can be frozen whole and used a handful at a time. Mostly though I try to have year round crops, so brassicas, leeks etc in the winter, and all the summer favourites kept to the summer - gives you something to look forward to.
I've never tried canning/bottling. My mother used to store a lot of produce in Kilner jars, but every year she lost some when the seal failed. There is also a danger of botulism. They seem to be more into canning into tins in the US, so that's where to look for hints. I'm not sure where you would get canning equipment in the UK.