Hmmm how long is a piece of string I'm afraid.
OK first of all. Congratulations on your baby. :)
How old is little one? Are you getting support from the infant feeding team at your hospital? Have you been discharged from midwife care?
If you are still in the first few days then droplets is exactly right and normal, and I would actually carry on hand expressing and see if you can collect in a syringe. You can buy 1ml or 2ml syringes from a pharmacy, or order online (medical/food grade) and then refrigerate or freeze these. I found trying to use an electric pump with this level of milk supply absolutely frustrating as most of the milk will just get stuck in the workings of the pump and dry up before you can hoover it out. For hand expressing, you need the "marmet technique".
If you are past the first week or so and you are still only getting droplets, or you want to use the pump to stimulate supply and are not really bothered about saving droplets that come out, you just want to get supply up, then go straight to the pump. You will want to look up the recommended pumping rhythm, from memory. Depending on the pump, it might do this pattern for you automatically or you might need to do it yourself. I found this quite baffling and frustrating but I did get there and having the right technique can really help. Also, doing things to help encourage a letdown such as looking at your baby, thinking about your baby, smelling your baby's clothes or looking at videos/photos of them. If you can pump while actually holding the baby then super! But I think I would have found that very difficult.
Don't over-pump. 10 mins each side is enough, even if you're not producing much by doing this. It's a good idea to do that every 3-4 hours. You will likely see your production increase over a few days, so don't get discouraged if you're not making very much to begin with. Most people find that it increases from a few droplets to 5-10 ml per session right up to 30ml per session or even more.
I would strongly suggest getting RL help and getting a feeding plan in place. Whether that is the infant feeding team/midwife team from hospital, or a private IBCLC.
You might want to look up about paced feeding - I found this enormously reassuring when I was mixed feeding DS2 because I found myself so stressed all the time at the idea he was taking so much formula that I would never ever be able to catch up and satiate his appetite. Paced feeding reassured me that he was only taking as much as he needed to, and not extra due to the bottle. It also meant that I had confidence to put him to the boob loads - like as much as he would tolerate basically, every minute that I wasn't sleeping/eating/showering and he wasn't being changed or bottle fed, I would have him on the boob. I didn't worry about him wearing himself out (because he was losing weight, I was under instruction not to let him feed for too long before adding the top up, which I didn't immediately understand, but I do now) so I would let him do his active feeding for however long on each side, burp, top up, and then after the top up let him latch on again and feed for as long as he liked, even if he was asleep but still latched on. It all seemed to do the trick. To be honest I never was very responsive to a pump so I stopped pumping very quickly.
OTOH if reading that makes you feel stressed and paced feeding is just another thing to worry about - forget it, it doesn't matter at all, the baby being fed is important and not how. Concentrate on whichever parts of this you have the energy for.