First of all, as a new player, don’t bother unlocking the Naxxramas adventures for gold. Either buy them outright or ignore them. In a few days the rewards from them will be limited to a Wild mode that goes live, a mode not intended for new players. I know you want to play solo and all, but this is still worth knowing since (except for one quest exception and a few one-off achievement rewards) you can’t earn quest gold in solo mode, and you’ll want to focus on being competitive in Standard if you ever plan to earn more gold/packs to play with.
Secondly, Naxxramas adventure wings won’t be purchaseable or unlockable after the 25th, so if you are going to unlock it you better do it before then.
You get the first wing of Naxxramas for free, but you better hurry up and unlock it if you want it. You can unlock subsequent wings for 700 gold each, but to unlock any after April 25th (for gold) you’ll have to unlock the first wing. Or you can just buy outright with money.
Anyway, you can unlock adventure wings for Naxxramas, League of Explorers, and Blackrock Mountain for 700 gold per wing. Each wing gives a minimum of one legendary and some other cards for most adventures.
You will earn gold by playing competitively. You can each 40-100 gold a day with repeatable daily quests (and one daily quest just outright gives a pack of cards), and you can also earn up to another 100 gold a day (enough to buy a pack of cards) by winning competitive matches (10 gold per 3 victories).
Also, as a new player, there are a bunch of ways to unlock card packs as you go, some of them solo, some of them competitively. Read this and find out how you can get up to 25ish classic card packs worth of gold and packs as one-off achievement rewards. That link also details the possible gold rewards for various quests.
Finally, even if you want to play solo, you really need to do the weekly brawl as much as possible, your first victory of the week gives one card-pack outright as a reward, and Brawls are the best way for new players to advance and feel competitive many weeks. But to play Brawl you must get at least one class up to level 20, which is pretty easy to do.
Finally, as already mentioned in this thread, if you login during the promotional period next week you will get a free legendary, 2 free epics, and up to 13 Old Gods expansion card-packs for logging in and doing a couple quests you’ll be given.