Something weird is going on with blockchain.info. All my transactions and $ balance are reading as infinity symbols.

I did a wire transfer to a USD back account in the UK. It took 2 days to process on Bitstamp and 5 days to arrive.

The last couple of weeks has seen Russia out, Apple out, Paypal out, withdrawal problems on exchanges, technical issues with bitcoin and large scale DDOS attacks. The price has only dropped ~17%. Anyone who sees this as weakness needs to have a rethink.

There are sites that say they offer what you are looking for but you are more likely to fall victim to a scam than find a profitable trader willing to sell shares.

I'd recommend buying and holding. The trick is to find somewhere you can buy $500 worth without paying too much. Before you buy have a look at https://bitcoinaverage.com/#USD. Make sure the price you're paying isn't much higher than this. 

In terms of return/hour you are much better buying and holding atm imo. Mining research is time consuming and returns aren't what they used to be.

As for buying you can maximize your investment buy picking the cheapest exchange and buying when that exchange is cheapest relative to the other exchanges. I would recommend spreading your investment across the 3 or 4 main cryptocurrencies. These track BTC fairly closely but give you more diversification.

I'd go with 70% BTC, 15%LTC, 15%PPC. You can purchase all of these at BTC-e which is also cheaper on average than the other main exchanges.

Before you buy look at the prices on http://bitcoinity.org/markets and check the other exchanges. If BTC-e is the cheapest then it's a fine time to buy. If not you're better off waiting a day or 2.