If you care about battery life, then you should not use linear regulators.
Linear regulators throw the voltage difference as heat which means you'll get very low power efficiency.
So let's say you have this:
[ 9v battery ] --------> [ 5v regulator ] -----------> [ 3.3v regulator]
Your device will use around 100mA from 3.3v so that means the 5v regulator needs to provide 100 mA to the 3.3v regulator.
This means you're using at least 5v x 100mA = 500mW to deliver 330 mW to your device. The difference (170mW) is wasted as heat, so that's 35% loss.
In order for the 5v regulator to produce 100mA for the 3.3v regulator it needs to take 100mA from the 9v battery, so that's 9v x 0.1 = 900mW going in, 500mW going out ... so basically almost half of your energy is getting lost as heat on the regulators.
LD33V seems to be a "nickname" for a a regulator from the *1117 series of linear regulators. These regulators require a capacitor on the output with a ESR value between 0.1 ohm and 1 ohm and something like at least 10uF of capacitors.
Higher capacitance than the minimum recommended won't hurt (in any significant way), but you have to be careful with capacitor type. Ceramic capacitors have very low ESR so if you want to use such capacitor (let's say to save space) sometimes it makes sense to add a small resistor in series with the capacitor to fake out a higher ESR ... for example add a 0.27 ohm resistor in series.
Tantalum capacitors will often have a higher than 0.1 ohm esr and they're relatively stable and small size, but they're expensive.
Electrolytic capacitors ... if you go with something like let's say 10uF 6.3v, the ESR of such capacitor could be higher than 1 ohm.
But you don't have to go with the minimum capacitance and the minimum voltage rating higher than the one you need.
For example, you could easily go with something like 33uF or 47uF rated for 16v or 25v maximum voltage from a low ESR modern series, and you can use one of these for both the 5v regulator and the 3.3v regulator.
The diameter and height of such capacitor won't be much bigger than the ones of lower voltage rating (6.3v, 10v) but it's enough to get the ESR within 0.1 - 1ohm.
See for example
Panasonic FC series - 47uF 25v is 5mmx11mm and has an ESR value of ~0.8 ohm , or
Rubycon ZL series - 47uF 25v is 5mmx11mm and 0.3 ohm esr ,,, these would be considered entry level / base low esr capacitors, there's much higher performance/ultra low esr capacitors nowadays but linear regulators don't need such high end capacitors.
You should redesign your project to use 5v from a power adapter, this way you can reuse cheap 5v phone chargers.
Some of those will output slightly more, like 5.5v so you may still want to use a very low drop linear regulator to stabilize the voltage to 5v
See for example
LP3985 or
NCP603.