Tiger Barb Tankmates

You need to plan carefully around tiger barbs.

The first thing to say is that they do better in larger groups - at least 10 of them. This keeps their nippiness within the group. When there are less of them they include other fish in the tank in their hierarchy set up and maintenance, and those other fish come off badly.
One option is to have only tiger barbs. This is not as boring as it sounds because they do come in three colours - the natural orange with black stripes, and the selectively bred dark green, and pale orange with white stripes. So for example, 6 of each colour would take you to about three quarters stocked and look like three different types of fish, though they'd behave as one big shoal.

Bottom dwellers are not usually a problem so a shoal of small loaches would go well with them. In 125 litres you are restricted to dwarf chain loaches as most other species are too big, although these fish do better in water that is softer with a lower pH than yours.
Bristlenose plecs would also be fine with them.
Tetras are a possibility but you would need to choose from those species that could cope with your water.

Fish to avoid include those with big fins (eg guppies) and slow swimming fish (eg gouramis).

I started with 10 Tiger barbs as suggested so that they wouldn't pick on the weaker ones so much. Not so, one by one the weakest were attacked mercilessly. This didn't happen for several months until they became adult size, everything looked fine at first. Black Ruby barb males are also very nippy to each other, but seem tougher and survive OK with nipped fins. I'd only keep the quieter barbs if I were starting over, my favourites are Odessa.