Welcome to CivFanatics dallasrocks!

I'm pleased that you're enjoying the game.
The technologies that start to open up opportunities to tech' towards the modern units are (arguably) Physics and Steam Power, so keep them in mind when considering your technology tree.
You can do a lot of damage in any era, but chasing Steam Power puts you on a path to Chemistry, and is only a technology away from Steel ... giving you Grenadiers and Cannons ... which can really cause some mischief when in packs (Stacks of Doom - SoDs). You can use these Industrial Age units to expand your empire while tech'-ing towards more modern units for upgrading.
When starting out, consider the land you've been given and the technologies that you start with. If you've got a coastal start, some seafood close by, and begin with Fishing, then a Work Boat might be your best bet. If you have a Grasslands-Gems resource and know Mining, then a Worker would seemingly be a good move. Every situation is a little different.
If you've yet to read it,
Sisiutil's Guide is a terrific resource for newer players.
Enjoy!