It's just a temporary inconvenience, except in a singular case.

Basically, all that a familiar's death means is that you'll have to recast Find Familiar at your earliest convenience (so it means the loss of a spell slot for a day if you have a time pressure and can't take the extra 10 minutes to cast it as a ritual). The spell/ritual does cost 10gp, but that's a pretty trivial amount for an adventurer. It also has a casting time of 1 hr so your party probably needs a short rest while you do it rather than simply doing it between encounters.

The only case where having a familiar come to harm is a permanent issue is in the rare event that you decided to retrain the spell (or as a wizard, have lost the spell book that contains it). These are the only times when losing a familiar has long term ramifications.

As to whether or not the newfound familiar obtained when you recast the spell is the same being reincarnated/resurrected, or a different being entirely, this is up to you and the flavor you choose for your familiar.

Before committing to this route, ask the GM if the campaign will even accommodate a PC using during play the skill Craft. Many campaigns don't or can't accommodate mundane crafting well at all because mundane crafting takes a long time—a basic sword can take weeks and an expensive, extravagant item made of special materials can take from several months to over a year of constant work. Even a master armorer or weaponsmith often finds it more convenient to purchase his gear instead of making his own. (The Craft skill can be used untrained, though, so it's totally legit to compose a character background saying that a character was, like, a weaponsmith's apprentice before he started adventuring yet the character possesses no ranks in Craft (weapons), quitting his master before he took any ranks. That's a thing.)

Tools and raw materials make crafting happen

Assuming the GM's campaign supports mundane crafting, as other answers mention, at least improvised tools if not artisan's tools or better are needed to practice a craft. These are abstracted sets of generic tools needed by a craftsman to practice the craft. Unless the GM rules otherwise, these are all the tools needed to practice the Craft skill. A separate anvil, for instance, shouldn't be necessary unless hunting roadrunners or needed for a feat. Also, usually tools and weapons are separate things—a warhammer suitable for bashing in orc skulls may not be a good tool for hammering steel.

Keep in mind that each set of artisan's tools is good for but one Craft skill—artisan's tools for the Craft (armor) skill are not also applicable to the Craft (weapons) skill, for example. Luckily, Craft skills are broad—the the Craft (armor) skills covers all armor and shields from studded leather to heavy wooden shields to full plate and the Craft (weapons) skill covers melee weapons from quarterstaffs to flails to greatswords—so the tools are broad, too. To create a quarterstaff a craftsman does not need artisan tools for both Craft (carpentry) and Craft (weapons), for instance.

Extrapolating from existing rules: Additional crafting requirements

A creator that's creating magic armor or a magic weapon needs "a heat source and some iron, wood, or leatherworking tools." It's not unreasonable for the GM to mandate that a craftsman that's crafting mundane armor or a mundane weapon meet the same requirements.

This GM views the required tools as part of an appropriate artisan's kit, not requiring, instead or in addition to artisan tools for the skill Craft (armor) a separate new and different set of artisan's tools for the skill Craft (leather goods) if creating or crafting magical or mundane leather armor, for example.

However, this GM also view the necessary heat source as needing to be significant—attempting to blacksmith up a greatsword over a flickering candle is a futile endeavor, for example. Fortunately, in most places where a craftsman plans to craft, finding a roaring fire shouldn't be a big deal. (In a pinch, I'm certain another PC'll arson something up for you.)

Finally, a craftsman usually can't make something that costs something from nothing, so a craftsman typically also needs raw materials. These are the abstracted parts that are needed to create the item, and these raw materials usually cost 1/3 the cost of the finished item. For instance, a longsword costs 15 gp, so the raw materials for a longsword cost 5 gp. Ask the GM if a craftsman buys raw materials that are either generic and can be used to craft whatever or broad and can be used to craft anything within a certain skill or specific and raw materials must be purchased for each item the craftsman intends to create. With the looming potential of an accounting headache, pray it's not the last.