So I'v tried over and over to get to the first town in the game, but the enemies I face all have far better weapons, range, and aim than my characters. My starting weapons feel about as effective as trying to hurl wet lumps of paper. I can't even get into the first town and my spirit is pretty broken right now. Any tips?

I have tried this game too, and it really feels like I am mostly running out of action points and outnumbered / undergeared. What makes things even more difficult is that my mercs are actually hitting the targets only sometimes. Also the "you are out of effective weapon range" message gets into my nerves, because it feels like I have to go really close before I am in the effective range. I want to hit the targets, so I go too near and die.
Well, reading the manual helps and trying to be more careful. Aiming is better when I right click the target, then it spends more action points to the shots. Also while moving when I hold down the del key, I see is the terrain safe (green) or dangerous (red). What makes moving more difficult is that if I don't see the enemy and I crawl to a safe spot, then I see the enemy and the spot is in fact now dangerous or deadly.
I try to think up some tactics, like its safer where is more cover. Its not worthy to run into an open area and just get killed. Two people could stay prone and give cover fire, though that is not much use if they miss all the time. They could crawl forward too, but shooting takes more action points after moving. Critically wounded enemies might flee a bit, but its necessary to kill them too, because they still shoot back.
I use the novice difficulty, but that doesn't make things easy. I can defeat 2 enemies without dieing. I learned to bandage after battles too. Then there comes more and more enemies at once and I am in trouble before I get to the city. This game is an expansion pack and usually expansion packs are more difficult than the plain versions. Reading the manual even more might help, I guess.
And save often. Also couple of times the clock mouse pointer has stuck, so I have had to kill the process and load.

The first time I played this game, I assumed that I could stand in the open and shoot the enemy with the accuracy they did to me. I finished the entry town with two dead mercs and the others walking like a zombie with broken arms.
After getting obliterated in town#2 trying to retake the airport, I restarted and tried again.
Now, after three long days of playing, and a team of 4 mercs I'm beginning to move on to the final city.
Keep at it! I still end up playing and getting fustrated, with all the saving and reloading, but a short 10 minute break between zones does wonders.
Things that have helped.
Hide around corners, shoot at the ground to attract the enemy. You can line up your troops so that one is on their stomach near the corner, one kneels behind them and another stands behind that one (At least until their marksmenship skill is 95+, otherwise I found you'll just hit your own mercs).
This is most handy when you bet a good burst weapon.
Use the stance option and the stealth option! Creep around! Hide behind rocks, trees, crawl through buildings or any kind of cover. Take a shot at the enemy then hide behind cover.
About half of the enemy troops will run towards you to get a better shot, making it easier to hit them on the next round. The other half are smart and will circle around you and take you out, so be sure to provide cover fire.
Before engaging in battle, have a good look at the map. In towns at least, take a good look at how windows and doors face other buildings. You can plan things out so that you can cover most areas fairly well once you have long range rifles.

i would recommend attacking at night if your weapons don't have long range, at night the vision field its very reduced for both you and the enemy (night goggles comes in handy) and
they will have to be close to shoot at you, and then you don't have the disadvantage of the low range, and if you don't see them that don't mean that they aren't there, go with caution and cover your back ;)

Attack at night. Put your best marksmen with good long range weapons in safe spots, while using other mercs to hit&run, luring enemies into killzones. Then throw some flares.