With thicker gauges strings there is more tension present, due to the fact the windings of the string are thicker, so they will require slightly more force to play, especially for techniques such as plucking or bending.Thick string gauges, e.g a 050 for your g string can have the potential to sound "deeper" as you desire, but ultimately all brands of strings, no matter what, can only sound so deep to a certain extent as long as they are in standard (EADG) tuning.They will sound like a "guitar" because they are meant to be tuned to that specific high key. If you truly want that "bass" sound rather than that "guitar" sound you speak of, I'd suggest two things: downtuning (dropping your string tunings to lower keys) or using flatwound strings (brands such as La Bella make good ones) With flatwounds you get less of the twangy brightness of most conventional strings and more of the deeper vintage "thunk". Flats do however, require some time to age, or "break in" as we say. But once they do break in, they can start sounding like this:
As for "beginner" string types, I'm afraid there is no such thing, for they are all the same in terms of "difficulty" if there is such a thing. Its mostly comes down to you testing the different strings brands until you arrive on one you like. In my experience, when I require a more deeper sound, some Steve Harris Signature Rotosounds (gauges 50, 75, 95, 110) can do quite nicely when strung onto a P bass.
However, to achieve that deep sound ultimately comes down to not the strings, but more on how you play technique wise, the various aspects and elements of your instrument, and your amp. Some wood and pickup combinations can lend you a very bright twangy tone, while others will lend you a deeper more rounded tone. Amp size, brand and type also can greatly affect how "deep" our tone will be. Some amps, called tube amps, give a more vintage tone, and what many consider "deeper".