Do you (or anyone else) know if there is a way of classifying gismu, as in: these types of gismu have this kind of place structure, and this sort has this structure... ? To memorize them with much more ease?
There hasn't been much success at organizing them! The way that I organize them in my own mind is basically a few categories based on complexity:
1. Simple ones. Ones with only one place, such as the colors, or with a conventional second place like all of the animals and plants (the x2 is always the species). There are a lot of these, which should be reassuring! "ninmu" for instance just means "x1 is a woman", no place structure to worry about.
2. Two place gismu describing an action. These are somewhat similar structurally to English verbs. Many of them are easy to remember because they have the same places as equivalent English verbs, for instance "prami" is "x1 loves x2", which is pretty much the same place structure as the verb "love", and "citka" is "x1 eats x2", which is similar to the verb "eat".
3. Gismu with weird extra places. For instance "palku", pants, isn't just "x1 is a pair of pants", but has an x2 place for the material of the pants, and "palci", evil, isn't just "x1 is evil", but has an x2 place for the standard by which the x1 is evil. The trick with gismu like this is to ignore the later places! Everyone uses "palci" all the time these days, and probably at least half of those people have never put any thought into its x2 place, as it doesn't come up. So don't feel like you "don't know" a gismu if you don't know it to the end of its places; if you know that "palku" means pants, you're doing fine (and if you also knew that "mapni" means cotton, you'd probably guess what "lo palku be lo mapni" means, anyway).
4. Big gismu. Four and five placers. These are the intimidating ones that inspire a posting here once every couple of months saying that Lojban's place structure system is madness. :) But notice that they're not all of the gismu or even the bulk of them. I think of the few 4/5 place gismu that I'm fully comfortable with as a small collection of unusually powerful swiss-army-like tools. The first one that I learned well was "klama" (which I've recently deepened my connection to by getting friendly with the BAI "ka'a"). Then I picked up "cusku", and "fanva". I have a few more now but those are still the large ones that pop effortlessly to mind. They're more of an occasional treat than the meat-and-potatoes of gismu! They're certainly not the main obstacle in learning to deal with place structures.
So that's sort of the categorization I have for them myself. Plus there's a lot of specific things, like knowing that living things have a species in the x2 or that a materials place is common for objects, etc.
As far as tips for memorizing gismu places, this is my tip: Please don't! Or at least don't judge your Lojban progress on whether you've successfully memorized deep gismu places. In my experience a much more common and easier way to actually learn the places of a gismu is one place at a time, in the process of learning & speaking.
For instance, I didn't ever learn the gismu "cfipu" by memorizing all three places at once, and I'm sure that would have been a bit intimidating. I remember learning the first place, a confusing situation, as if the gismu were just "x1 is a confusing situation". Then I learned the second place, the person who's confused, and I started to use "cfipu" as if it just meant "x1 is a situation which is confusing to x2". (I also remember taking a while getting comfortable with different arrangements of the first two places, such as "mi se cfipu", I'm confused.) Finally I picked up the third place, the quality of the situation which is confusing, and now I'm comfortable with the whole real structure, "x1 is a situation which confuses x2 because of its property of being x3". I've only been to that point for a few months, though, and "cfipu" was serving me well in partial form for years!
So that's my main advice to gismu learners: Sure it's intimidating to learn a five-place gismu, or even a three-place gismu, but you're not really expected to learn all the places of all the gismu at once, you know? If you're learning "klama", don't worry about memorizing the 3rd 4th 5th places, start by being comfortable with "x1 goes to destination x2" and work your way up from there.