I've noticed that a lot of people have a misconception about crypto currencies. From what I've seen, many people who look at crypto currencies, bitcoin in particular, probably since it's the big dawg on the block, by it's particular coin's equivalent fiat value. Most people seems to associate crypto currencies with stocks and think that you must purchase an entire unit. Well, I'm here to tell you that you don't. Crypto currencies are like fiat currencies, as they are fractional, with the difference being that most crypto currencies are fictionalized to up to 8 decimal place (0.00000000), which means that you can hold an amount of crypto currency at a fraction of a penny.
With that being said, you can get in the "crypto-sphere" with any amount of money. As far as making an investment with a tight budget, my best suggestion is to just start making small purchases of crypto currencies, as I did. Maybe buy $10 - $50 at a time (the more you buy the better, as you will pay a fee in most cases when buy crypto currencies, as well most crypto currencies have fees upon transferring, let say from and exchange to your wallet). The two best options would be either buy your crypto on Coinbase (easiest to use, easiest and quickest to be verified on) and/or find friend that are holding and trading crypto currencies, the later being the best option as it creates communities in the crypto space.
The best option starting is to spread your purchases across several coins, maybe 3 -6 strong coins, in order to diversify your portfolio and protect against down turns to DCA (dollar cost average). Definite do you're research before jumping. Read white paper, get familiar with trading (even if you're just HODLing).
The main thing is to be patient. Just like any other investment, any major profits will not most like be soon, unless you're day trading and luck up on some quick pump and dumps at just the right time.