Hello everyone,
I am planning to travel for around 3 months January-March next year and don't know where to begin with budgets,routes etc. I would prefer the East coast of Australia if I had to narrow it down due to timing,
I have some money saved but I am wondering how much money to save up in general and where to begin looking for hostels etc. I am in need of a lot of help haha
I'd consider January-March the worst time of the year to visit Australia, with the wet season up north (going from unpleasantly humid around Brisbane, to frequent torrential rains in Cairns) - you might remember news about flooding from previous years - and really very hot days further south - you might remember news about bush fires.
Of course, you might luck out and not experience any of that next year, but if you can alter the timing of your trip, that's what I'd recommend (next to doing New Zealand instead). 
Ignoring that warning for the remainder of this post, and speaking in generalities: It might pay to get a hostel membership for your local version of hostelling international (which in Australia is called YHA), and staying mostly at their hostels - assuming they fit your idea of an ideal hostel (they tend to be less party-oriented; their big flagship locations are pretty expensive and anonymous, while their smaller locations tend to have more personality - but all of them have a pretty decent minimal level of cleanliness and comfort). There's a ton of alternative independent options around, though, some serving more alternative and/or party-oriented crowds, and some being on the same level as - or surpassing - YHAs. Reading a recent lonely planet is probably still a good bet for getting a feel for what's out there.
Pre-covid, Australia tended to be pretty expensive, particular in the big cities. I have no idea what the situation is these days, but I'd expect it to still be the same, with you needing to count on a budget of at least AUD $100 / day for staying in hostels, buying supermarket food to cook your own meals in the kitchens there, travelling from location to location by bus/train about once a week, and doing the occasional activity (think platypus spotting rather than skydiving). Call it AUD $10,000 for the entire three months to be on the safe side, assuming you're capable of living somewhat frugally. If you want to splurge, you can easily spend more than double that without trying hard.
For transport, Greyhound busses have the largest network, and a one of their travel passes might be worth it, just to save on hassle. But there's a lot of cheaper regional alternatives as well. North to south or south to north doesn't really matter; just follow the coast, since there's very little when you move inland.
Personally I enjoyed the south of Australia most (Sydney, Melbourne, Great Ocean Road, Grampians, Tasmania, as well as the far southwest (below Perth)). Personal highlights on the east coast for me were Eungella National park (with the platypus spotting) west of Mackay, Magnetic Island (near Townsville) and Mossman Gorge (north of Cairns)