The UCLA Phonetics Lab has a public database of how sounds are used in different languages. There is also a nice website UI for the database, hosted by the University of Frankfurt. This contains a browser that can look up which sounds are used in which classes of languages.
For example, you can see that languages classified as Indo-European are:
ALBANIAN, ARMENIAN, BENGALI, BRETON, BULGARIAN, FARSI, FRENCH, GERMAN, GREEK, HINDI-URDU, IRISH, KASHMIRI, KONKANI, KURDISH, LITHUANIAN, NEPALI, NORWEGIAN, ORMURI, PASHTO, ROMANIAN, RUSSIAN, SINHALESE, SPANISH
You can then go see which sounds these languages use. For example, German uses these sounds:
p b k g pf f v s z S Z x m N l R h i: y: e: o/: E: a: u: o: I Y E "@ 4 U O j E) ai Oi au d ts n t
All of which have a special phonetic name associated with them. You could use this information to differentiate your new language in many ways. Here are a couple I thought of:
1. Use completely different sounds
This is the obvious way, but may be rather difficult as the Indo-European language class covers a very wide variety of sounds. You could look through and see which sounds are not used and make them the cornerstone of your new language. A potential downside to this is that written language often can sound many different ways. Even if you use different sounds, they may look similar on paper.
2. Use a smaller set of sounds
You might notice that Indo-European languages contain a very broad set of sounds. One way you could differentiate your language is to limit the amount of sounds. For example, Hawaiian uses a much smaller set:
p k ? m "n h "l w i E a "o u
Hawaiian's repetitive vowel sounds and consonants make it feel very different from German, even though they share much of the same phonemes. You could make your language feel unique by choosing a novel subset of sounds. This has the added benefit of allowing your language to be accessible to a Indo-European reader.