There are a LOT of great tools out there.
Usability Hub
I love using Usability Hub because I can set up a test at the beginning of a meeting and have the results by the end of the meeting. I used it mostly for preference testing between two alternatives or for first click testing to see if people would know where to start a process. I would most often pick a sample size of 50.
Learn more about Usability Hub
UserTesting.com
I used this tool both in corporate life and in teaching. It allows for a webiste to be provided, questions presented one at a time, and the ability to record the participant going through the site and answering the questions. I would use it for unmoderated user tests.
For example, one could ask someone to fill out an online application and make comments throughout the process. Also, one could ask what someone would EXPECT to see on a page, click on that page, and then indicate their reaction on what they saw compared to what they expected.
For students I would have them run 3 rounds of tests.
Round 1: For the first round I would introduce them to the tool, we would use the existing website as the baseline model, I would give them the questions to enter, and I would walk them through how to analyze and present the results.
Round 2: For the second round, they would provide their own updated website, they would use comparator questions from the baseline site, and I would help them create additional questions. Guidance was given on how to report the changes from baseline to updated site.
Round 3: For the third round, the students provided the questions, the updated site, the updated questions, and presented their results.
UserZoom
I liked using UserZoom for moderated online tests where I would want to select a panel of people and administer questions to them directly. One of the benefits of using this model is that we would not have the logistic issue of bringing people into a lab setting. It also allowed for us to do deeper dives or explore different emergent flows.