Red Cherry Shrimp are by far the easiest shrimp to keep, they will breed but the tetras will more than likely have a field day hunting and eating the tiny shrimplets so the population should only grow slowly. Cherry shrimp are also good in that they come in a range of colours, just be aware that the more expensive the colour usually means the harder to keep and that due to line breeding to establish the colour morph the other colours can have less vigour and be fussier in water paramaters.
Colours include
Red Cherry - Sakura
Fire Red
Bloody Mary
Blue - Velvet
Diamond
Black
Chocolate
Green
Yellow
Orange- Sunkist
Rilli - this are being developed in almost all of the colours listed above.
The temptation is great to mix all the colours together and have a "rainbow" tank of shrimp but this a really bad idea since the resulting offspring will in almost every case not look like any of the parents instead they will revert to dull wild type shrimp that people only want as live for certain fish.