Keeping sufficient recovery time between the dives is very important at serial diving. Keep the surface time about 2 times the last dive time. Having a freediving computer greatly facilitates watching for the times - it displays both last dive time and the current surface time. Freedivers tend to shorten the recovery if they do not watch for it.
However, definitely forget about any "breath-up" when recreationally diving. The only result will be that you start hyperventilating (even if you do not think you do) and start pushing closer to your physiological limits, exposing you so to the risk of blackout seriously. All you need at recreational diving is resting and calming you down when you are on the surface. When I watch newbies, I always see them excited, swimming there and back, diving back down a few seconds just after surfacing, hyperventilating (although they claim they don't), etc. Any unnecessary physical effort on the surface decreases oxygen saturation of the tissue, increases CO2 and lactic acid levels, increases metabolism and heart rate, and leads to much shorter dive times.
Experienced freediver, spearfisher, or snorkeler will barely move on the surface, propulsing with only very gentle fin (or hand) movents. Besides better preparing so for the next dive, your chance to see something under water are much higher than when running after every fish you spot.
The experienced recreational freediver will also breath very quietly without putting any focus on the breathing. Definitely no hyperventilation, purges, big deep breaths, or any other forced ventilation. The body will take care about just the perfect oxygenation of your organism automatically (assuming you are calm). Any attempt to control it will just mess it up and you will be either hyperventilated or not ventilated enough (hypoxic / hypoventilated). Of course, you need a few deep breaths after surfacing, but also here that comes automatically, and you should not try suppressing the need for clearing your lungs after the dive. Let the body do what it needs.
So you best stop thinking about any breathing, and instead of it put your focus on better relaxing you, calming down, and resting. The proper breathing will come automatically with it, and the risk to be hit by blackout will be lower too. In contrary, if you are excited, stressed, or feel fear or nervously, the body will react with hyperventilation automatically too, so if you observe any such sign, be sure to calm down first.
