Most electronics shopping involves parametric searches. To use these effectively you need to know the terminology, which makes it difficult to get started, but a lot can be inferred with a bit of common sense. As a start, I'll work from the two mainstay distributors, Digikey and Mouser. Both links point to sections dedicated to enclosures. It's also useful to review manufacturer websites, Hammond Manufacturing and Bud Industries are two of the largest manufacturers.
To start, it's important to note that there are several types of enclosures. Note that the terminology is not particularly standardized:
- Cases are small, a few inches on a side, usually designed to sit on a desk or in the hand. They're usually made of extruded aluminum or plastic. They usually contain one PCB, mounted on rails or screw mounts built into the case.
- Enclosures are larger are intended to be wall-mounted or freestanding on the floor. The larger ones often have knockouts (circular perforations that can be removed with a screwdriver, pliers, or hammer) for wiring to enter and exit, contain internal wiring, internal components are often mounted are often mounted on DIN rail, They are usually made of folded sheet metal. The distribution center in your basement is one example. Their selection is probably specified for you by the IEC (or, in the USA, by NEMA (the National Electrical Manufacturers Association)), and there are many regulations surrounding their use. If you're working with this equipment, you'll need more education than a simple answer here can provide you with.
- Racks are towers in which equipment meeting a standard profile can be mounted. 19" server racks are one example, though they might also contain test and measurement equipment, PLCs, or other electronics.
Since you mentioned a 'small electronics project that includes a micro-controller[sic] and a few extra items soldered down to a PCB' I'll assume you want a case.
Digikey calls cases 'boxes', and has a number of subordinate 'container types', including bin, box, cabinet, case, chassis, console, and housing. Mouser's Enclosures, Boxes, Cases category has slightly more descriptive 'product' types, including boxes, cases, commercial enclosures, desktop enclosures, electronic instrument enclosures, etc. No definitions are given, so eliminate the ones which obviously don't apply and leave all the rest (ctrl-click to select multiple items). Move on to the other categories.
Both sites have a rating criteria with IP numbers. These numbers specify not the Internet Protocol address, but the Internal Protection rating - the ability of the case to keep water, dust, and fingers away from the items inside. The specification (IEC 60529, Table of Contents here) is over $200, but decent overviews are available on Wikipedia and from other manufacturers like Altech. Let's assume that you want some minor protection against dirt and water (what else is a case for, anyways?) and go with an IP 54 or 65 rating. You could also allow higher ratings, but this still returns a couple thousand results, so we'll work with it.
Material should be obvious. There are two basic categories: Metal and Plastic. Conductive plastic blurs the line somewhat. Use metal if you want something sturdier and/or conductive. Plastic is usually cheaper.
Most cases use one of two designs. The simplest design is an open-top box. You can filter to these on Digikey by selecting the design type "Cover Included" or "Split Sides"; Mouser doesn't seem to have such a filter. These boxes usually have hollow pedestals on the base to which you can screw your PCB. The cover then gets screwed on top of the box. A slightly more complicated design is the tube with end caps. These usually have grooves in the side, and the PCB is slid down the grooves. If you have horizontal connectors on one side or two opposite sides of your board, the extruded design can work nicely (cut holes in the end caps), but if you have any other configuration, the open-top box is much easier to assemble.
I don't think you'll need any help on the definition of 'size'. Most of these boxes are rectangular, so length, width, and height are somewhat interchangeable. I've not found any sites that do a good job of letting you search for a size; while you might want to specify a set of minimum and maximum dimensions, the sites invariably ask you to choose the precise size, which immediately narrows your search to 1 result. Use multiple selection judiciously. This is often the most time-consuming step, so save it for last when previous selections have removed some sizes. Remember that you'll probably need extra space for wiring, panel-mounted parts, and hardware, and that larger enclosures dissipate heat better. Smaller is only better in industrial design and in weight/volume constrained environments; it's almost never better for the assembler/PCB designer.
Once you work through this process; it's just a matter of scrolling through the options. Hopefully you've narrowed it down to a reasonable number of options in the above steps!