How should I invest $10,000 in crypto-currency?
I'm going to assume Bitcoin since that is by far the most common cryptocurrency by mindshare for people who are new to the space.

Since you have $10k to invest, you could buy around 5 to 7 bitcoin mining rigs with a capacity of 13 to 16 tera-hashes per second each.  Investing in these mining rigs will give you about 1 year of mining time before the rigs cost more money to run than they can make.  You could make approximately $10,000 to $30,000 profit during that time assuming you have cheap electricity, and buy 5 x 15 TH/sec bitminers.  This path requires far more technical knowledge than a simple purchase of  bitcoin.  To get 5 mining rigs for $10k, you'll need to buy direct from a manufacturer.  Bitcoin mining rig manufacturers typically require a wait of 3 or 4 months until delivery.

If you buy bitcoin, you might lose the entire investment if bitcoin goes to zero; on the other hand you might make 10 times your investment if bitcoin repeats the past 12 months of performance.  If you stay invested for a longer timeframe that risk/return is extended.

There is no simple answer to your question since it depends on your technical knowledge, risk appetite, and timeline.