Custard based ice cream vs eggless ice cream
The two types of ice cream are generally referred to by name as:


Philadelphia style.  No eggs.
French style.  Custard based.


Each can produce a quality product.  

Philadelphia style ice cream is easier to make, as it is not necessary to make the custard, and it can have very pure, clean flavors.  Its mouthfeel is critically dependent on the quality of cream, and the way it is churned and frozen (even more so than French style).

French style ice cream has a smooth almost silky texture, due to the natural emulsifiers in the egg yolks, as well as a distinctive eggy or custard like background flavor.  It is also somewhat more work to make, and the egg flavor can compete with other flavorings.

There is no way to give you a single recommendation, as both types of ice cream have their advantages.   For pure, single note flavors like a delicate fruit or coffee, you may wish to go with Philadelphia style.   For maximum richness and decadence, especially for deep chocolate and vanilla flavor, French style is very good.

There is no reason to exclusively make one or the other; you can have recipes from both types in your repertoire.

Either way, the quality of your product will be enhanced by making the base mix the day before, and refrigerating it over night before churning.

See related:


Why does holding ice cream mix improve flavor?