You picked a good forum to ask your question. I have seen many of the comments in action. Keep in mind that if you are trying to get started, a move might be necessary. If you are truly flexible, you might try contracting for a while.
Another option is to pursue the advanced degree of your choice. In other words, don't pursue a Ph.D. unless you are truly excited about the topic. In my case, I really got excited about fatigue and fracture of metals late in my undergrad years. I decided to stick around for a masters to do materials testing and finite element analysis. My interest level deepened the more I did and pretty soon I was well on my way to a Ph.D.
Once I completed my Ph.D. program, I hired on to a major airframer, which required a move, as an entry level engineer when they "weren't hiring". Within my first year, this airframer went through a major layoff but I was retained. Within three years, I was back in a lab environment as a lead engineer.
After nearly 8 years, multiple layoffs, and a 6 week strike, I chose to take all my training and practical experience and move back to a more geographically pleasing location. This placed me in totally different engineering environment outside a lab but still associated loosely with fatigue and fracture of metals but in a community where I was essentially an unknown quantity. In order to to this though, I took a pay cut and a position without leadership responsibility. For me, the pay cut was only a small issue and the lack of leadership responsibility was a relief. One year later, I was able to get a promotion and exceed what I would have been making had I stayed at my first engineering job.
In my opinion, the following points are important.
Focus your technical training on what you enjoy technically.
Be willing to move to get yourself established.
Focus on your goals, not a pay check, status, etc.
Demonstrate your capability and let it speak for itself.
If you find the employment experience at one location isn't working out, don't be afraid to make a change even if it is into a different facet of your specific area of expertise.
Take your job seriously but balance that with a genuine interest in what your are doing so you can truly enjoy your job.
Contacts are certainly beneficial but they are not, necessarily, a requirement.
Good luck,
ML Thomsen