What type of bike should I get? I am about 200lbs 5'6 woman, 47yrs. Attached a screenshot of my last bike ride. It was mostly flat road, 2 lane country/ city bike paths (included was a 30 min layover where I grabbed a Snickers because I could feel I needed (energy?).  I like to ride but this was my longest bike ride ever attempted and included a 5km detour (where I took a wrong turn and became lost). That's the background. 

I like to ride my bike I have now is a Specialized (Hard Rock) 19yrs old where last year I switched the mtn bike tires out for street just to make the bike lighter. I love riding long distances and hate going to the gym. I am a stay at home mom so the only other exercise I get is from the TV to the Kitchen and back. My intention is to start riding regularly.  I see these people out on my bike rides and they are riding Canondales etc. and are whizzing past me.  I can't help thinking maybe if I had a better / lighter bike, I could get around more easier. Surely technology has changed in 19 yrs? My husband says he won't shell out the money for a racing bike because he thinks it's overkill however I take this as he doesn't think I'm serious. My intention is to get fit and I am anal about comparing my speed records against myself ie.. I intend to make my laps in shorter time. 

I want a good bike not a cheap bike one that will last me a long time that I can take on long rides. I should add the area I am in now is Scandinavia (Denmark) and no there are no bike lanes where I'm riding they are two lane roads. Looking to spend between $500 area.
First - a lot has changed in 19 years, but not much. Some bikes are lighter, faster (and a lot more expensive) than 20 years ago. The difference between your Hardrock and a new one today is small enough not to matter for most people most of the time. 

I am with @Blam this - if just wanting to get fit its arguable a heavy slow bike is better - its certainly cheaper than upgrading.  

If comparing against yourself is the goal, any bike will do. 

If comparing against others, one thing is more satisfying than passing some random cashed up middle aged exec wannabe on a $10000 super bike on your 20yo Hardrock - seeing their face as you do it.

If racing against others and winning is your goal, you need a new bike. If keeping up with a group is a problem to the extend you do not enjoy it, a new bike would be a wise investment. 

Valid reasons for a new bike is if the Hardrock is a poor fit and/or you are uncomfortable riding it. If the Hardrock is worn out (many 19yo bikes have less miles than many 19day old bikes, so age is not a good guide) it may be better to replace it than spend money fixing it. 

Another valid reason is if, having put down hard earned money - against your husbands wishes, it makes you feel bad about not using it and motivates you to keep riding where you would have stopped riding had you not upgraded (i.e. it gives you the will power to keep riding). 

One good reason not to replace it just yet - wait till you have a few more miles under your belt, and have established a pattern of use. At the moment you are getting into it. You may find you like single trail MTB riding, or get into 100km road rides. In a few months you will know how you are using your bike not how you plan to use it. 

By not changing the bike, you don't have to ask 100 questions (What kind of bike, what brand, how much to spend.....) that have no correct answer.