I completely agree!! Having grown up with short-term missions in my youth group and now as a full-time missionary Short-term trips are amazing and can be very impactful. I think some of the downfall is when you don't partner with local missionaries or organizations because there isn't that built in follow-up.
Another thing to be aware of is that the local missionaries and organizations know the needs and culture of the place you are going so it is best to work WITH them instead of insisting on doing things your way because it may hinder instead of help.
For first time trips, partner with a missions organization that does this (such as YWAM, Mission Adventures or AIM). These types of organizations set up trips for groups like you all the time and have for years (some as long as 50) and have access to locations around the world!! They are on the ground and will remain after you are done. There is also the opportunity to build relationship with those missionaries and continue pouring into their ministries long after you have left.