How much of a self-starter are you? How willing are you to put in a few weeks of going out every day and night in a town and introducing yourself for locals and seeking out opportunities? Will you be scared to hop on a chicken bus with the locals and wish you had someone to pick you up in a nice comfy van? Do you know the language?
I'm very biased against voluntourism agencies. I worked with one in the past, I will try to search up links to some old posts when I have more time. Basically, I witnessed firsthand people getting ripped off by hundreds of dollars per week and getting nothing out of it. I went with a local NGO that charged me $15/day for room and board. Everyone else there was paying companies like i-to-i hundreds of dollars per week for the exact same room and board. And honestly, the only difference was that they got to file their paperwork with native English speakers. Most of them didn't even get airport pickup and transportation to the project site. And the people who were in control of our particular project made some decisions that made me lose respect for them to the extent that I didn't want to provide free labor to them, as well as made me feel like staying there would be a huge detriment to my experience of the local culture. Basically they forbade us from interacting with the locals and they also forced me to work on an extra project other than the one I was assigned to, then kicked me out (I was planning to leave anyways, had just found a hotel to move into) when I complained to the person who was in charge of their organization (the person who told me I only had to do my project, not the other). When I left the project I found plenty of volunteering opportunities and the locals and local expats were very nice and welcoming. But, I did go out every night and have a genuine love for the town, and I didn't have the condescending attitude that I think a lot of well-intentioned western volunteers go with -- the "I'm here to do meaningful work, and not to party and surf and drink beer in the middle of the day" attitude. Well, in Costa Rica, the locals like to party and surf and drink beer during the day so if you're not willing to do one or two of these things with them they aren't going to like or trust you. Especially the expats who are a tremendous resource in hooking you up with opportunities. (At least in the rural surf type towns. Could be different in the mountains or agricultural towns.) If you're shy, you don't really fit into the local culture, or you're scared in developing countries (some countries warrant this fear, most are safer than the US), you probably won't have the same experience.
So yeah, I wouldn't go through a voluntourism organization OR any local NGO that required me to live in their facilities. If you only have a couple weeks to volunteer, then going through an organization is pretty much your only option, you won't get the locals' trust or be able to make a contribution during that time frame anyways. But even then, you can make a better contribution to your chosen community's society by going on a nice vacation there and spending the money you would be giving to a US or UK-based tourism company in the local economy. I think the average voluntourism vacation in Costa Rica is roughly $400/week -- you could have an awesome time in nice accommodations, eating out, renting surfboards or dive equipment, for that money, rather than living in an open-air shack with 20 people to a room and intermittently functioning toilets, AND you will benefit the local community MORE, especially if you target local-owned (instead of expat-owned) restaurants and environmentally friendly hotels and lodges. In my opinion, voluntourism is generally only worth it if you truly think you'll enjoy the experience more than the vacation you could buy with the same amount of money
Editing to add: I had also never been out of the country before this, so you don't need a lot of international experience. I'm definitely not intimidated by much travel-wise, but you certainly don't have to go on a bunch of tours before you can do it on your own. Just be confident and curious.