Getting faster on the bike

For longer term development, look into training methods and appropriate tools for them early on. Developing your fitness is an on-going process. Equipment changes can be made along the way. Also remember that these things aren't really entirely in isolation from one another either.

Like Ben said, there are lots of different ways you can achieve better bike splits (i.e. get faster).  None of them are free - either you pay for them in $$ or sweat, and it's been my experience that there's a better ROI on the latter. 

If you don't have a trainer, that's a great investment.  Being able to ride indoors provides a weather-free and safe environment to train.  Getting a good bike fit is a good investment, properly balancing comfort vs. power vs. aerodynamics.

The three ways to get faster on the bike are to improve fitness, get better equipment or a more aerodynamic setup, and to improve your bike handling and confidence in going fast.  Usually buying equipment and getting a more aerodynamic setup can be done while you're not training or improving your handling skills, so it's not an either/or decision on which you decide to do.  You can do BOTH if you want to!  

Improving fitness and handling skills take a lot of work and a lot of time, but in general it is either free or of low cost (if you're doing some type of trainer software or something).  It usually yields the biggest gains for someone new to cycling though.

Equipment choices and setup are generally a quick fix, and cost a bit or a lot of money.  But once you get the benefit, it doesn't bear more fruit over time like improving fitness does.

So to me the best approach is to work on everything you can afford to work on.  And for some people, time, not money, is the real limiter so there is no shame in spending money to buy speed if you're already maximizing your available time to train.

Jason said some on this too. The ROI on the latter works more as fitness keeps building on top of prior fitness. So the earlier that gets attention, the more the gains can be. A lot of equipment tends make a more static or fixed amount of gain. It's definitely there, but once you have it, it's not really going to develop more. Having a well fitting bike (not necessarily a highly aero one), can be a bit of both as it is equipment, but can also help with training more & better while also being able to utilize fitness better.