CCEA is excellent cluster analysis software, a vast upgrade from what you can do in SPSS. We have extensive training documentation and even training videos on our website. Our software has extensive documentation and help functionality built in and our technical support group is extremely responsive and helpful. Of course there is also this forum as yet another way to get answers to any questions you might have about using the CCEA software.
We do offer a package called Latent Class. Please be aware that is specifically for latent class multinomial logit - in other words it simultaneously runs a choice model and the latent class segmentation, so your data needs to be choice experiment data with a categorical dependent variable and several observations of choice per respondent.
If you are looking for software that does general latent class modeling (no dependent variable, no repeated choices per person) analogous to cluster analysis the commercial package Latent Gold, sold by Statistical Innovations is a good way to go (see their website) and you can of course get free latent class packages in R, though of course these won't come with as much support for you to learn them.