I am hoping (b'li neder) to start, relatively soon, a regular regimen of study of the Talmud Bavli. My goal is to learn large swaths of the g'mara, gaining broad knowledge, but without taking the time to go deeply into it, so I'll probably stick to Rashi as commentator for the most part. Unfortunately, I will probably need to do this alone, without a chavrusa, and I'm worried — indeed I'm sure — that I'm going to get stuck at certain points. Having an ArtScroll g'mara at hand would be helpful at such times, but I don't want to buy every volume of the ArtScroll g'mara — I mention this just so you can get an idea, if you're familiar with the ArtScroll g'mara, of the kind of resource I seek. Can anyone recommend a free Internet resource that explains the g'mara clearly and fully, and that allows me to find a section or line of g'mara easily? (That last criterion would exclude most audio lectures, since it's hard to find where in the lecture a certain passage is discussed.)
Firstly hatzlocho on this very worthwhile endeavour!
There are a wealth of resources online which collectively can provide anything from a basic translation to a more in-depth review and more. I am not sure if there is one website in isolation that will give you everything you want but you may want to peruse the following options below to see what works best for you:
Sefaria - It breaks the daf into easy, digestible parts with clear translation. It also also links to various commentaries at the click of a button (although many are without English translation)
dafyomi.co.il - this is a fantastic resource which allows you to select a given masechta and cycle through a number of options per each daf. For example, if we take the option of Berachos here, it gives you the option to see a full review, explore insights on the daf, view English charts, tosafos, Q&A's etc.
Daf Digest - Provides really good overviews of each daf as well as some deeper thoughts on some select pieces, including a 'halacha highlight' and 'stories from the daf'
The Steinsaltz Center - Provide a daf by daf selection with a clear and succinct overview of the prevalent theme on each daf.
Daf Notes - Provides clear summaries and more
All Daf - Made up of predominantly video and audio which I know you said you wanted to avoid, but there is also an invaluable series of 'reference materials' provided as well including daf review, daf insights, quizzes, halacha outlines etc.
I recently discovered Shas Illuminated which while not having a line-by-line breakdown and daf navigation like some of the other sites I listed, nevertheless provides numerous shiurim on that day's daf as well notes on the daf too which I find brings a great deal of clarity to the given sugya (for example here). There is a tremendous list of maggidei shiur available and has several high-profile haskomos
Finally, and thanks to @rosends there is also Mercava which gives you complete control over the daf (including Rashi and Tosafos) with not only translation but also a breakdown of the text detailing if the words are a statement, proof, attack, defence, question and answer.
Besides Dov's impressive list, I highly recommend Daf HaChaim. It's a shiur on every daf, with useful diagrams and very clear explanations. Regarding your concern about not knowing where on the page the shiur is holding, the site has a visual image of the daf and shows you which piece the shiur is discussing.