Would it be wise to begin investing into this plan?
Provided you have no other consumer/educational debt to take care of first, yes.
How does it work when I leave my current place of employment?
You own the investment even after you leave your employer (voluntarily or involuntarily). Most people will either roll it to an IRA account or to their new employer's retirement plan.
Will I be able to continue investing in the account at a later date or is it essentially abandoned?
It's not abandoned - you still own the account and can roll it into a different account, but you can't directly contribute to it anymore. You will either contribute to your new employer's retirement account (403(b) or 401(k)), or an IRA.
Also, since you admittedly don't know much about these plans, remember that they are designed for retirement, which means that there are significant penalties for withdrawing the funds prior to retirement age (currently 59 1/2). you can change investments within the plan as much as you want, and can roll it to a different retirement plan without paying tax.
Finally, it doesn't really matter right now what you invest in within the plan. Start to educate yourself on the different options (mutual funds, index funds, target-date funds, etc.), and when you know better what you want to invest in, you can "rebalance" your portfolio for a more long-term strategy. In other words, if you choose a less-than-optimal fund on day 1, you're not locked in forever, you can change it later. Since you will have at least 35 years for it to grow, just contributing as much as you can is MUCH more impactful today than choosing the "right" fund. Even if you change your funds in two years, you _still _ have 33+ years of growth that will more than make up for the 2 years of opportunity cost.