Deciding to the clustering algorithm for the dataset containing both categorical and numerical variables
The best thing to try is hierarchical agglomerative clustering with a distance metric such as Gower's.
Mixed data with different scales usually does not work in any statistical meaningful way. You have too many weights to choose, so no result will be statistically well founded, but largely a result of your weighting. So it's impossible to argue that some result is the "true" clustering. Don't expect the results to be very good thus.
I am a newbie in machine learning and trying to make a segmentation with clustering algorithms. However, Since my dataset has both categorical variables (such as gender, marital status, preferred social media platform etc) as well as numerical variables ( average expenditure, age, income etc.), I could not decide which algorithms worth to focus on.
Which one should I try: fuzzy c means, k-medoids, or latent class to compare with k-means++? which ones would yield better results for these type of mixed datasets?
Bonus question: Should I try to do clustering without dimensionality reduction? or should I use PCA or K-PCA in any case to decrease dimensions? Also, how can I understand and interpret results without visualization if the dataset has more than 3 dimensions ?