I plan to take several courses/classes through various acting schools (not Uni) in the U.K. It’s my understanding that I need a visa, not just a US passport, to study any amount of time, and that a Standard Visitor visa would allow for only 30 days of study. A Short-Term Student visa would allow for <6 months of study (which cannot be extended) and a Tier 4 visa would allow for >6 months vtudy (which can be extended). Is that all correct? Thank you.
The gov.uk website is surprisingly well designed and clearly describes the benefits and limitations of all of these visas. I highly recommend investigating the resources they have posted there, some of which I link below, because they're quite informative and well presented.
A Standard Visitor Visa allows up to 30 days of study, but it cannot be the primary purpose of your visit. The primary purpose must be leisure, business, or certain other limited reasons (including sports, creative events, seeking medical treatment, etc). This visa can be extended, so long as the total time spent in the UK does not exceed 6 months.
A Short Term Study Visa is for non-EEA citizens who are involved in a short course of study. It is limited to 6 months for any short course, or to 11 months if you're over 16 and taking an English language course. It also has some limitations on where you're studying, for example you cannot be studying at a publicly funded university.
A Tier 4 visa is for non-EEA students who have been offered a place in a course. How long this visa is valid depends on numerous factors which are detailed here. Note, however, that the courses one takes must meet certain qualifying standards in order to make you eligible for this visa; see section 53 on the pdf that details the visa specifics. These visas are off-topic for this site, and questions regarding them should be asked on our sister site Expatriates.
The school or schools you're applying to may have further guidance on the subject, and may be able to recommend one visa or another, or to give you specifics related to the program that will help you determine if you qualify for the Tier 4 visa.