I agree with the comments about Stanley Fat Maxes for "site"/DIY work - I find the through tang and striking caps make them ideal for lots of types of work. They aren't the best for keeping an edge (although they are better than the Irwin-Marples copies I've tried), so it is necessary to touch them up from time to time (for which you'll need a combi stone and probably a honing jig), but they will take a heck of a lot of abuse, including being hit with a steel hammer - a real no-no for wooden handle chisels. On site I do use them for shallow mortising, but TBH if I need to do a lot of hand mortising I'll generally get out my roll of Crown and Sorby registered mortise chisels (I have a mixture, butb only sizes I regularly use) which are quicker and easier to use on deep mortises because they are stronger and are a lot less prone to twisting in the cut. They should ideally be driven with a wooden mallet. If you do start out with the Fat Maxes then something like 6, 12, 18 and 25mm should cover most of your early needs
Workshop Heaven sells some truly wonderful stuff, at a price. I bought a set of Ashley Iles mkII bevel edge chisels from them a few years back for bench work and they are possibly the finest chisels I've ever had with a really thin blade (in other wods proper bevel edge chisels, not firmers with the edges knocked off), but unless you are a professional woodworker £200 plus for a set of chisels is a tad overkill. In any case you probably won't get the benefit until you have mastered the basics of woodworking. Either way try to buy only what you need for the next project rather than buying a big set which you'll never use - and spend time to learn how to sharpen and hone them properly first because once that becomes more or less automatic you can get in with the real task of making stuff
M&T joints are normally glued. There are unglued versions, such as the tusk tenon, but they aren't really suitable for the application you have in mind