There’s nothing that keeps a player from reaching legend as a f2p, but you often have to be frugal with your collection habits and play by dust, or try to aim to overperform over a listed 50% wr if you need to get through the d4-legend chamber.
I’m a f2p myself, and although i think i remember my first year distinctly remembering my attempts to counter boom with boulderfist ogres couldn’t do jack, i still remember that there were plenty of f2p accessible (though probably) boring decks like early midrange shaman.
(Which i’m not even sure if it USED any legendaries… Except maybe Aya in MSOG, just since Aya was too many free good stats then i think)
For the most part, playing f2p, you want to craft around your collection and be frugal with dust, and also pilot decks. Ideally, diamond 5 i think is the sweetspot of minimal effort, optimal rewards for time even if you can reach legend.
There’s no bonus stars and it’s not uncommon for people to spend 10-30+ hrs on the legend grind if not the entire month for some as the winstreak bonus ends and it’s all just 50% wr decks and players getting very competitive over that last d1 to legend final boss bracket.
For the most part, the two main things you can do are try to get better, look at optimal trades, tempo, view what makes your deck wins certain matchups.
And also while mundane, you can’t just really throw together anything random and win with it in standard past gold 5 or diamond 5 most of the time usually.
Even offmeta stuff at least still needs to use the basic class’s 5-20/30 basic good cards or so. For rogues those are secret passages, scabbs, and often ± Prep.
For warrior you might as well have every pirate and pirate quest on the list, and to make pally work you need a 10000-16000 dust or a credit card ready to tribute summon pally for 100-160$ dollars in face down position.
While people see netdecking as a copy paste thing, when you’re f2p, it can often be a great way to see how close you are to a deck by uploading your collection’s data to hsreplay to see which decks are closest. In my Case, my opens were Quest Shaman (Nerfed), Quest Druid, Quest warrior (Sucked prebuff, now used), as well as a pretty late quest rogue quest all f2p.
(My other legendaries were Auctioneer jaxon, boogeymonster, mogor the ogre(aka Boulderfist ogre but BGH’ed and worse), and wing commander ichman.
From the 3-4 good quests, i can see that for the most part, i was able to make a quest shaman for the first few legends and tweaked it when it was a little lower on the meta charts.
(Got nerfed), After that, i think i found out i could make a deathrattle dh for 1.6k (fell out of meta), after that, i had a cheap f2p elemental shaman. And after the deadmines buffs i could run budget pirate warrior lists.
I have to say, if you were looking at a cheap budget list, pirate warrior while often boring tends to always be good, but it’s always on a nerf radar right now so im not sure.
Technicality wise, 1.6k dust is about the cheapest you can go and it’s a deck that will ladder up to diamond 5 easily. Legend is a bit iffier and it doesn’t go to 1k legend, But it’s a pretty cheap and solid deck. If it doesn’t get nerfed soon.
But blizzard has a recent habit of doing half mana nerfs that don’t really change the meta right now. so 
. You don’t know if it’ll be axed enough to fall from like a 50% wr to 44% like the first quest shaman nerfs, or if it’ll keep slogging on like handlock’s several nerfs.
I’d probably wait until the next nerf notes before crafting a new deck though. I think Thief rogue and pirate warrior will make any deck crafted now, shaped around a thief rogue and pirate warrior meta. And some decks good at farming one might not be good in another meta.