You don't need to change your resonant (bottom) heads but if they are old, worn, or damaged then it is a good idea. Also, changing from stock heads to quality aftermarket from Evans, Remo, or Aquarian will certainly increase quality of sound, though if you are newer to drums I wouldn't both right now. Hydraulic heads are very easy to tune and give a fat thumpy sound, as Evans describes them they are great for less experienced/newer drummers and/or problem drums. One thing you should be aware of though is they do not necessarily give a softer sound. They cut out a lot of overtones making the sound of your drums much more like what you are used to hearing on radio pop songs (you will hear this described as "pre-eq'ed") from your ear at the seat but they do have a very pronounced 'clicky' sound to them (you will hear this described as "stick sound") which is even worse with nylon tipped sticks. Contrary to popular belief, they do not make your drums quieter. They can reduce overtones that travel long distances and they can reduce the ability for your drums to 'cut' or project but, to a neighbor for example, your drums will be just as loud.
All in all I think hydraulics are a great starting point for new drummers. Even if you end up preferring a more open (read: ringy, resonant, etc) sound down the line these will get you started, are very durable, and will allow you to focus on playing your drums and NOT spend all your time fiddling with tuning and muffling. Slap em on, tighten them (in a star pattern) until they sound pleasing, then have some fun!
One way to control the 'ring' of a drum is to place a cut-out circle from another worn out head on the batter head.
The cut-out would have the main part of the head and the outer ring/bend of the head removed...just an inch or so remaining out on the edge.
When you strike the head, the 'loose' cut-out 'levitates' up removing the dampening(mostly) then as the head loses energy from the strike the cut-out settles in and gives a form of mechanical compression....reducing the perception of sustain while not over-choking the freq made by the drum or forcing you to look at amplification/recording in order to apply compression effects.
Obviously not as useful on a drum that has the head surface vertical to gravity(like a bass drum) but my experiments allowed me to set the tom to 45 degrees...and a bit more...while the rim prevented the cut-out from becoming a frisbee.
Another thing I wish I would have been exposed to earlier is the technique of playing by using your fingers...have a look out on youtube ...loads of demos...and i think i was in my 30's before I observed the technique and found some of it in what I was doing.
Lastly, the technique of striking the drum will dramatically change the sound quality...you can control the ringing of a drum by 'softening' or 'hardening' your hands and allowing the stick to have a bit more or less contact with the head(or cymbal) after the strike...it can be difficult but like most things becomes second nature....kinda like palm muting or variable string pressure on a guitar. It now feels like I am flamming pressure on the surface just after the original strike...with different degrees of pressure attack and sustain...often allowing the head to throw the stick off once the struck surface reaches the desired velocity range.
Welcome to the forum...looking forward to your perspectives through your adventure!
(edited to try and give the results of my experiments - hopefully reducing effort for others)
What also can be a suggestion is coated heads top and bottom. That gives you a warm sound and the coating adds some more muffling/less ring.
Never tried that myself, but people swear by them combo.
Check out some videos by Benny Greb to get an idea (he also uses cotton balls in his floor tom to lower the sustain).