The writing system is called Devanagari and Sanskrit and other languages use it. Sanskrit has various extra symbols for sounds that aren't in Hindi. Devanagari has 50+ characters depending on how you count them. The basic ones are fairly easy to learn because they are phonetic and the syllabary is in an order that makes sense. The consonant sounds progress in order based on where in the throat/mouth they are produced.
Edit: I forgot to mention the conjunct consonants. There are a lot, but I wouldn’t recommend trying to memorize them. They can generally be recognized by looking at the combined shape and seeing what consonants made them up. Not memorizing them won’t impede your initial learning. A few of them don’t look obvious what made them up like क्ष and ज्ञ so those are better to study more.
I'm not sure what you mean by the other method, maybe romanized with latin characters. You're probably going to need to learn the basics of that, but its very easy since the characters are phonetic. There's a few romanization systems, for example the character आ is the sound ɑː and is transliterated as ā in many systems, and aa in another common one.
Also Hindi grammar is fairly straightforward once you get used to the subject object verb order. There are very few irregular verbs as well.
Hindi is often classified under 'lesser learned languages'. You'll find there are far less resources for learning Hindi than other languages with as many speakers, but you can find plenty on the internet if you search enough. I found various websites to help learn and practice Devanagari and it's sounds, even including some that showed the stroke order for writing the characters. And of course, there's thousands of Bollywood films you can watch with subtitles for getting practice.