There is absolutely nothing wrong with worshiping the Gods in a modern language. If you want to perform your blots in Japanese, Swahili, or Klingon, great. The important thing is that you are worshiping the Gods. However, many Asatruar feel more comfortable in a Northern or Western Germanic language, especially the older ones.

If a particular language doesn't call to you, you can pick based on the needs of your group. If your group is more northerly, you may want to learn Icelandic. There are plenty of resources available for learning Icelandic and it is very similar to Old Norse. If your group tends toward Saxon, then consider Old Saxon (Old English). For a more modern Western Germanic language, you can look at Dutch, Frisian, or German.

Even if you don't become fluent in the language, a greater knowledge of the language will help show connections between concepts that would have been available to early Heathens. You may learn quite a bit.

From a purely theatrical side, you can gain a lot of Heathen points with the younger folk if can occasionally mutter in an ancient language.