Yes, you need a players handbook. Based on experiences with previous editions, there will be a lot of books expanding those rules, especially new feats, but the PHB lays the groundwork.
Please note that both feats and multi classing are optional rules that you don't need to play the game.
By the rules, no. The Pact of the Chain says:
You learn the find familiar spell and can cast it as a ritual. The spell doesn't count against your number of spells known.
When you cast the spell, you can choose one of the normal forms for your familiar or one of the following special forms: imp, pseudodragon, quasit, or sprite.
And the find familiar spell says:
You gain the service of a familiar, a spirit that takes an animal form you choose: bat, cat, crab, frog (toad), hawk, lizard, octopus, owl, poisonous snake, fish (quipper), rat, raven, sea horse, spider, or weasel.
The list of which creatures you can use as a familiar is highly specific, and doesn't include either the Wolf or the Dire Wolf.
That said, some of the options available to a Pact of the Chain warlock are quite a bit more powerful than a Wolf. The Imp and the Quasit are both CR 1 to a Wolf's CR 1/4, with spellcasting abilities to boot, so a generous DM might be willing to stretch a point and let you use a Wolf instead, particularly if it's appropriate for a character. I suspect a Dire Wolf is probably out of the question, though.
There is another potential alternative: If you took 3 levels of Ranger, you could get an Animal Companion, for which a Wolf is an option. Depending on your character, a Ranger might fit as a substitute for Rogue. A character for whom a Wolf familiar makes sense sounds a bit Ranger-ish to me. Only you know what you want your character to be, both mechanically and thematically, so I can't really advise you too much here.
Best Answer
If none of the backgrounds in the Player's Handbook (p. 124-141), or the Sword Coast Adventurer's Guide (p. 145-154) seem to fit you, discuss with your Dungeon Master(DM) a custom background. Once you determine why none of them fit, your DM may be able to show you how one does fit, or help you create a custom background as explained on page 289 of the Dungeon Master's Guide. There is also the "mix and match" approach (p. 125 PHB) where one swaps features between backgrounds already presented to get a custom background fit for your character. Work with your DM (it's a collaborative approach) to get the fit "just right" for your character and the campaign.
Each background comes as a package. It typically includes:
Read through a few of the already created backgrounds to get an idea how these fit together.
I'd suggest comparing the Sailor, the Criminal, the Folk Hero, the Guild Artisan, the Sage, and the Outlander to see how different packages are assembled. When you and your DM mix the elements together for your background, that will keep it consistent with the Background feature at your table for those who picked one from the pre-built backgrounds.
The Personality Traits, Ideals, Bonds,and Flaws you can pick and choose from all of the various brief descriptions already in the Players Handbook, or try your hand at making a few in your own words. Whatever you do, work with your DM so that it all fits into the campaign world you are going to play in.
The point of this, of establishing a background, is that you enter your adventuring career as someone with a past, a past that for one reason or another led you to the adventuring life. This step in character creation helps you flesh out your role and gives you some touch points for role playing. Role playing evolves into the story of your character. As the story grows your character becomes some kind of hero in the context of the game world.
I have found that writing a brief story of "how I got here" helps me get a grip on who the character is. The background is a great starting point for beginning that "how I got here" story.
1 Tools and languages (pick a total of two) are part of the mix and match approach. Using the examples of Acolyte, Criminal, and Noble...
Acolyte: Skill Proficiencies: Insight, Religion
Languages: Two of your choice
Criminal: Skill Proficiencies: Deception, Stealth
Tool Proficiencies: One type of gaming set, thieves’ tools
Noble: Skill Proficiencies: History, Persuasion
Tool Proficiencies: One type of gaming set
Languages: One of your choice
(Source: PHB, Ch 4).