The Ciceros and Lyam Thomas Christopher have provided the most popular and accessible routes to self-initiation in the Golden Dawn tradition. I have things to say about both systems, but the upshot is that both work, both have different approaches, and it’s really a matter of personal preference. You can probably also mix and match effectively to some extent, you’ll just have to be proactive in understanding what part of the material is there for what reasons.
I’m familiar with both curricula: I actually started with the Ciceros’ SI book about 20 years ago when I was first getting into the system myself, back before I got into a more traditional temple setting, and I’ve read through LTC’s curriculum as well. The two have very different approaches.
Firstly, on an energetic level, both the Cicero route and the LTC route appear to “work”—which is to say, they both do the job of connecting you to the Golden Dawn Current. How they go about doing that differs, and the education they present alongside it differs almost as starkly. The strategy the Ciceros take is ceremonial, and if you’re drawn to the ritual aspects of the tradition that might resonate better with you. LTC takes a more meditation-based approach. You get meditations in the Ciceros’ curriculum as well, they just don’t do quite the same heavy lifting.
LTC also departs a bit from the mainstream of the tradition in that he gives a lot of Adept magical work in the earlier grades, and in particular I look askance at his decision to use the unicursal hexagram in the Lesser Banishing Ritual of the Hexagram (it has precedent within the tradition, but it’s nonstandard). So LTC diverges from the mainstream not just in the way he handles the initiatory current, but also the traditional learning curriculum.
(To be clear, I don’t necessarily take issue with the way that LTC does this or the reasons for which he arrives at it, I just find that where he ends up at looks different from the Golden Dawn tradition the way I learned it in some manners that make me a bit uneasy—but this is my own bias and my feels, not something I’m arguing as a point either in favor or against.)
Both the Ciceros and LTC are fond of giving students a lot of busywork and information that isn’t directly pertinent to the alchemical operation of the grade energies of the Current, if you want to talk about what’s strictly necessary for the alchemical growth and development. If you look at the material you get tested on in the Ciceros’ SI book versus what you get tested on in traditional temple-based systems (I was a member of the Ciceros’ HOGD for about ten years, and was an Adept and a temple chief), you see that they require you to learn a lot more. Which I find problematic. But LTC isn’t any better on that front.
But again, both approaches work. I personally prefer and recommend the Ciceros’ SI book if you’re going to choose one over the other, just because it’s more representative of the wider tradition that other people are following; and if you’re working with the Ciceros’ material, you’ll find a lot of other people with the same foundation. It’s also easy to work LTC’s meditations into the Ciceros’ curriculum as well, or to use the Ciceros’ ritual self-initiations with LTC’s. I don’t think mixing and matching is at all an issue here.
So to sum up, the best thing to recommend the Ciceros’ course is that they follow the Regardie-traditional rubric common to most of the living Golden Dawn community, and being in step with that living Tradition is especially important to me. If you prefer solitary work or if you don’t plan on joining an order, that’s probably not going to be a factor for you.
Finally, a word on the commonly-stated advice that one shouldn’t practice other (non-GD) rituals when it comes to Outer Order curriculum. This advice can generally be read in two ways. Firstly, you’re trying to learn a language; so you want to avoid taking on too much information outside the GD system in order to avoid “muddying the waters” by confusing yourself or getting your wires crossed. And that’s entirely a matter for your own honest assessment of your capabilities. Some people have no problem studying multiple systems at once, some people do. Use your discretion. The second reason largely comes down to concerns about systems that may be at actual cross-purposes with each other. It’s perhaps debatable whether it actually does any harm to pursue GD and OTO initiation simultaneously, for example, but it’s generally considered a) weird, since Thelema rejects what it perceives as the Old Aeon; and b) bad form, because you’re splitting yourself thinly. This particular kind of objection may have more substance, but it’s a rarer situation—and even then debatable. Either way, it is probably not wise to “cross the streams” of multiple initiatory energies from multiple currents at the same time. Bottom line, assess your own capabilities and act accordingly. Nothing catastrophic is going to happen from attempting to study multiple systems at once.