Bill the diagram in the pdf is what it is because I havent figured out a better way. I know its frightening to look at. Distance is time, so if you wanted to guess the time from A to B on that diagram, use 3 minutes between stops and you will be pretty close.
Google Maps: The problem is that when using the transit mode, Google will not let you plan multi-stop trips. You can plan the individual legs then save the directions with a link (I send it to myself on WhatsApp). The other problem is that quite often it doesnt show the best option. For example if I want to go to the Great Market Hall, Google Maps will send me walking down Andrassy ut to the 47/49 tram, when the eaiest option is to take the M1 to the 47/49 tram and avoid the walk. The good news is that it will tell you which public transportation to get on and give you the end stop so you know which direction to get on. Also, what Dutch_traveler said about clicking on stops. Works most of the time.
BudapestGo: This app also has a trip planning mode and seems to present better choices, but again one stop at a time, you cant plan out the day. And you cant save the stops to pull up later.
The reason why the planning is so important here is that the tourist zone is very large and the destinations are well spread out. Good news, if you are into 19th and pre-WWII urban environments, and explorying the city between the stops is facintating. The great old architecture just goes on forever. But if you spend a little time planning you will discover that most of what you want to see will be on 3 or 4 trams and one metro line. You will also note that they cross so often that you can plan a trip with little or no back tracking or retracing steps.
How big is it? You will be working in an area of about 10 square miles. Prague and Vienna both have 90% of their top sights in about 1.5 square miles.
You can google "Tourist Map Budapest" and find maps like this that will help: https://maps-budapest.com/img/1200/budapest-walking-map.jpg and here is another good one https://www.isango.com/Files/map.jpg
The word "bus" got used a few times. I ride a few buses a day but I am not so much a tourist. Generally speaking a tourist will not have a lot of need for a bus. The most frequently used one by tourists is to get from Pest to the Castle in Buda. Otherwise the trams get to the vast majority of the sights. Of the trams, you probably will find yourself on the M1 a few times and if you are returning to either the Parliament or the Great Market Hall, you might use the M2 or M3 but there are trams that will get it done without putting you underground and where you can not see the city. Oh, and we have two types of busses. Regular Bus and the Trolly Bus (powered by an overhead electrical line) .... not that it matters.
If you will be here a few days, maybe the best thing you can do is to do a self instruction course on the system. Take the M1 down to the 47/49, then the 19/41 to the 4/6 and back to the M1. By the time you finish you will have traveled through the heart of Pest and along both river banks and will have changed trams / metro often enough to be a pro and feel confident.
Do be sure you have a pass. The fine isnt worth it and they dont take excuses.