While @mtoto is right and this is more suited to stats.stackexchange.com, as I happen to use R for business research, I'll give you my take as answer.
Unsupervised learning is not suitable for your objective. Customer segmenting absolutely has to be related to the business goals.
One question you can ask yourself to help guide the features to choose is, when you say "based on customer data", what data were gathered and why were those data gathered rather than other data? Usually the customer data are collected in the first place with some sort of business objective in mind. The result of your consideration may also be to refine the data collection process to only collect data relevant to your clustering (unless it's a larger pool of customer data that has many intended uses).
Customer segmentation is usually based on features that will predict product/service selection and quantity. All other features are usually less relevant to segmentation. The specifics depend on the nature of the products/services offered by your company and your customers' reactions to those products/services. If your goal is pricing strategy, i.e., determining optimal prices for different customer segments, then you'll want to focus on features that relate to the utility function of customers, i.e., the perceived value they get out of your product/service relative to the amount they pay. If your goal is product/service expansion, i.e., investigating where to add new products/services for customers, then you'll want to focus on features that relate to particular customer needs in the different segments and the pairing of your product/service to each of those needs, identifying gaps.
Once you've got your feature selection narrowed down to your business goals, start with basic linear models (or even just correlation) to validate your assumptions that those features are indeed related to the desired dependent variables. Once you've established correlation around core features, you can then add additional, plausibly-related features, and run clustering tests piecemeal to determine which other features are redundant (i.e., the same as the previously chosen core features) and which ones expand upon them in a way that increases the overall r^2 of the desired independent->dependent variable relationship. As you validate individual features in this manner, you can progressively build larger cluster models. These models are most useful for telling you when to not bother collecting/evaluating customer data that are barely incrementally different from other core factors.
At the end of the day, in my experience, there are usually very few features that relate to a particular business goal. In one project, I assessed around 46 different features, and only found 6 that mattered. That's also why unsupervised learning models aren't great--They try to hard to select too many features, and you end up with either spurious results, or results that are uninterpretable in terms of business actions to take--which is your whole purpose.