You can draft an independent claim for each system, and an independent claim for each method, as you mentioned.
The thing is that not every jurisdiction accepts more than one independent claim in a single application, or more than one independent claim per category in a single application; sometimes there are exceptions whereby you can include additional independent claims, but this is not applicable to all jurisdictions. Also, unity of invention objections could be raised against your multiple independent claims, thereby forcing you to pay additional fees and/or move some claims to another application. This depends on the criteria laid down by each jurisdiction for assessing when different claims or alternatives within a claim possess unity (you can have a lack of unity of invention in a single claim).
Sometimes there is no other way out than drafting an independent claim for each embodiment. But if there are features common to all embodiments that render the invention novel and non-obvious, perhaps you can have a single independent claim per category that encompasses the four embodiments, this way you can define each embodiment as a dependent claim. It could happen that the common features need to be defined functionally or in a more descriptive manner for them to encompass the embodiments, this in turn can lead to clarity issues or broad claims that are not novel or are obvious. You should assess how likely it is that you will run into such problems; the assessment may also be dependent upon the jurisdictions where you will seek protection and their claim requirements.
A broad independent claim encompassing all the embodiments, even if not novel or obvious, sometimes can be used as a strategy in the early stages of prosecution if, in turn, the patent office gets to examine the embodiments of the dependent claims. The examiner may be less reluctant to accept multiple independent claims if the embodiments are patentable, and with the previso that the patent laws of the jurisdiction allow you to have more than one independent claim in the application.
A word of advice is that you also include the method claim(s) as you mentioned. It is rather frequent that a system is not patentable but the method is.