Tamiya Extra Thin for most plastic, though on the harder compositions like that I've come across in Zoukei Mura kits I use EMA Plastic Weld.
I use bog standard CA glues (superglue) both thin and the gel types from supermarkets or similar. Don't buy expensive model specific CA glue, it's a waste of money. All CA glue goes off once exposed to air (well, technically the water in the air) and few will ever use a full container before this starts to affect the glues performance. I've never done so even building resin kits.
You can extend the life of the glue by keeping it in the fridge, unfortunately the Fuhrerin vetoed this option in my case, despite my well argued and factual argument, based on my old chemistry degree. For some inexplicable reason she was totally unimpressed with my knowledge of the relationship between rate of reaction and temperature!
Some kind of white glue is a must, I often use it for P-E parts which require a bit of wiggle time. At the moment I've got some Gator's Grip 'Acrylic Hobby Glue' on the go, which is very good, but there are cheaper options.
I use G-S Hypo Cement for clear parts. It's an easily manageable gel with a fine applicator, allows some wiggle time and sets to a strong bond in about a quarter of an hour. I've been using the same tube for years, so if you look after it you won't be buying much of it.
Finally, I have a two part quick epoxy handy. I rarely use this on models, I think I may have used it on a dodgy undercarriage recently, but it's a useful thing to have. It is also useful if you drop your mug and break off the handle
