How much of Heavensward can I access right off with a low level character

No, there's no mechanical benefit to having multiple characters. A few intangible benefits do exist, such as being able to try out the other starting nations' introductory quests, or try out a different race or gender.

Conversely, there are a number of benefits to leveling multiple classes on a single character. Due to the way the cross-class skill system is designed, leveling up multiple classes on a single character is highly beneficial. A character that largely focuses on a single class/job (leveling other classes only to the minimum required to unlock their preferred job) won't have access to important cross-class skills that can be extremely important, especially in higher-level content.

Additionally, when playing on a class that's lower-level than your highest-level class, you receive a 50% bonus to experience gained.

EDIT Alternately, you can use leves to grind your way to level 51 and buy yourself a set of HQ Archaeoskin XXX of Crafting from the market. Expensive gilwise but definitely the fastest way to go about it.

There are some one-star green items and jewelry that boost your crafting abilities as well.

I've found this link useful; as per this site's protocols I'll summarize here:

You will need to craft or obtain the following items at HQ, all of them at most one-star:

• Patrician's Wedge Cap (weaving)
• Dodore Doublet (leatherworking)
• Patrician's Gloves (weaving)
• Patrician's Bottoms (weaving)
• Patrician's Gaiters (weaving
• Raptorskin Merchant Purse (Leatherworking)
• Red Coral Earrings (goldsmithing)
• Militia Wristlets (goldsmithing)
• 2 Aetheryte Ring (goldsmithing)
• A whole lot of materia.

The trick is to overmeld absolutely everything as far as you can. This will be the most expensive part, as success chances start dropping quickly past the first overmeld; this image shows the optimum distribution that never hits the various items' stat caps:

At that point, the automated set of macros described in the article will all but guarantee 100% HQ on two-star items. They're a little more convoluted than I really want to put into this answer, though...