QGIS 3.2 Quick Map Services Plugin not Showing Basemaps

It shouldn't take hours for a basemap to load. It shouldn't even take more than a minute, and that's with a very slow internet connection. Loading time on my computer (with a mediocre internet connection and at least a 5 year old desktop) is less than a second.

In my experience, not all the basemaps listed in the quickmapservices plugin menu actually work. I don't think I've ever been able to load the landsat layer. Try a few different maps from different data providers. The maps from OSM, Google, Bing, Stamen, CartoDB and ESRI usually work for me. (Some of those are extra basemaps that you can get by installing the "contributed pack.")

Also try putting your project in WGS84 or WGS84/Web Mercator. The basemaps seem to load more quickly in their native CRS's, which is usually one of those two. (I haven't seen this documented anywhere, it's just based on my personal experience). Once you find a basemap that works you can change it back to the CRS you want.

Or, you can first load a local layer (eg, get a shapefile for the state/province/country/county/city where you'll be doing your mapping). Zoom to that layer, and test out different basemaps until you find one that works at that scale.