Welcome to Traditional Knives WarkerJ. You'll find a great community here and a real wealth of information. Would either of these knives be your first traditional knife?
A lot can be said about these two types of knives. You've got a lot of options for Case Stockman and a lot of option for Laguioles. Laguiole is a place in France, in the Aubrac region, so the name isn't trademarked as a brand name, but rather covers a type of knife that is widely imitated by companies around the world. These knives can vary widely in quality, but IMO you'll be best served by one made in the general region or from a fine French cutlery town like Thiers. I'm far from an expert on these knives and they're not the most common on here, though there are plenty of admirers for them here and I do count myself as one. If you're looking for a Lag I'd check out these companies for starters - Forge De Lagiuole and Laguiole En Aubrac. There are other very fine French producers, but these 2 companies are very authentic and offer models that would fit your budget.
Now before getting into a lengthy discussion of Laguiole producers, I'd start by identifying what its useful for. The standard model is rather long, usually around 5 inches with nearly a 4 inch blade. These knives are beautiful as well as strong, but from my own experience they are sort of more of a date night, special occasion knife. They excel as a portable steak knife when you're out to dinner, and the elegant filework and materials make it something of a conversation piece. That said I wouldn't necessarily choose it as my first general purpose Traditional as I would want to have something with at least 2 blades, one bigger and one smaller. If you're just carrying a Lag and you need to cut a loose thread from your coat in public, you are forced to flash a relatively huge knife for a task that requires a bit more discretion.
That brings me to the Stockman. The stockman will introduce you to 3 traditional blade types in one package. A medium stockman (around 3.5 inches closed) or a large stockman (around 4.25 inches) , will give you a clip (good for cutting apples and other food prep), a sheepsfoot (great for general utility) and typically a spey or pen blade (for smaller detailed cutting tasks. This makes it much more versatile. I would start with a mediuim or large stockman with CV (carbon) blades to get you used to oiling and caring for the blades and to get the experience of watching the blades patina with use. Case Stockman are also much cheaper, starting around 35 bucks, whereas the Laquiole will be closer to 80 or 90 bucks. The thing about the Stockman is its so useful with three blades in such a compact package that it may make you ask why you'd ever need another knife, but seeing as you're already planning to get a bunch of knives, I'm sure you'll find the will to resist satisfaction. LOL
Before getting a Laguiole you might consider another classic french knife, the Opinel, to start out. Available in many sizes with either carbon or stainless blades and very inexpensive. They even make a slim version that has a profile similar to the Laguiole. Another option is to try out some toothpicks as these knives share some common ancestry (up for some debate) with the Laquiole, as they're both derived from the navaja clasp knife.
I hope this is helpful as a start. I'm sure folks will pipe in with more specific recommendations as you refine your selection. There is a lot to be said and I just scratched the surface. Get ready LOL