If your on a tight budget like 70% of amaricans I'd do this
1. Get 2-3 penguin bio wheel 350s some people hate them because the bio wheel idc what they say I have a few they are GREAT filters for the price and 3 would keep a 125 spotless. Also there great workhorses I won't ever get rid of mine and iv had one going 24/7 365 days a year without ever being unplugged. They will be about 20-40$ each also the filter pads you can fit the cheap filter pads that Walmart carries fits in them. So really short run and long run you save money with the 350 bio wheel.
2. Grab a cheap 48" shop light from any hardware store. You can put full spectrum bulbs in them for plant growth and non plant bulbs so your not growing algae. 1 of them hold 2 48" bulbs so it will light your 125g up bright. And bulbs cost less then 10$ (full spectrum plant bulbs 2 for10$/ non plant bulbs both 4$)
Now if you got cash burning a hole in your pocket there's tons of ways to get what you want.
i think i want a fish. maybe two.
Cheapest route for lights is exactly what cory said. 48" shop light and put different bulbs in it for your needs.
Filters he's right again, for cheapness and effectiveness. But I prefer canisters for bigger tanks like these. I personally have the Fluval FX5 (brand new it's around 275-350) and I love it. Without a doubt, I'm looking at buying another soon just to keep in stock as well as full rebuild supplies.
" To reach manhood, we are all cast into the fire and purified by pain "
If you live in the united states black friday almost here if you can wait. I'd pick up a canister filter. In the long run your tank will look better, less maintenance, not a ton of crap hanging over your tank, and you just fill it up once with ceramic media and some prefilters. Never have to worry about buying filter pads over and over. Fluval x5 is 265 on a few sites know and when black friday hits most places have 10-20% off online sales.