Is it a better idea to funnel all that money to the loan payment and save a bit of interest,
or build my liquid savings and be able to kill the loan in one shot once I have enough saved? What factors play into this?
Letting the money sit in savings to earn less interest than your loan is accruing is not a good idea.
Ideally, you'd go with a mix of these strategies. Once you have savings sufficient to absorb an emergency, you should start funneling as much as you can toward that debt. The canned advice is generally $1,000 of emergency fund, but if you may need to move apartments and pay a security deposit or some such you may want to adjust that higher; but once you have your emergency fund established you prioritize the loan. AND emergency funds go in stable, liquid vehicles; savings account or maybe a CD. This money does not get put at risk to try to eek out a better return.
6 months of expenses makes a lot of sense. In a bind, you have 6 months of buffer to find a new position and settle in maybe even pay a headhunter to place you. You can make decisions based on the best decision rather than a need. At it's core, money gives you control of your decision making. This level of buffer is very important for breadwinners with mouths to feed.
I don't really know why I feel compelled to write this today, but here we go. To start, I'm a millennial. So don't read this as coming from a crotchety old baby-boomer who doesn't understand today's world. School was the easy part. If you're a young recent graduate.... go work. The start-up you worked for missed a funding round, neat, go find another one. Get on fiverr. Get on elance. Cold call businesses. A young person can find work. You might not like it, it might not be what you think you want to do. But you don't have an established career, you have only yourself to feed and clothe. Don't let yourself start carving out a rut of comfort. If it takes you 6 months to find work you are doing something wrong. Not work you want, not work you think is in your chosen career trajectory, just work. Put a grand in the bank that doesn't get touched unless the alternative is you missing work tomorrow.
Lets ignore the principle potion of your loan payments which do also zap your cash flow. $12,000 at 6.5% is $65 of interest each month. Put this in terms of the time you have to spend working for someone else, to pay yet another someone else. Based on national averages (about $72k per year of income taxed at an average effective rate of 13.5%) that's about 1.6 hours of net pay per month. Why does someone else already own that effort? Stop committing your future efforts to other people. Money is control. If you owe people money, guess who has the control... I guarantee it would be more fun to set that $65 on fire at the end of the month than it is to send it to the person you owe it to. That's control. That's what you want.