I don't know a thing about ComputerShare.com. But I can give general advice.
1) Maximize any free benefit from your employer. Free is free and is the best deal you will ever get in your life because in most cases it is many thousands of dollars absolutely free each year. Yet, a large amount of people who qualify pass it up.
2) Beyond whatever you need to do to get free stuff from your employer, you need to be quite careful about fees. No one in the world can perfectly predict the future and say that stock A will do better than stock B. But everyone in the world can say that stock A has such a high fee that it is unlikely to do well enough to do better than stock B. These could be fees to buy the stock, fees to sell the stock, and/or fees to hold the stock.
3) Fees over about 0.5% should be looked into very carefully. An annual fee of 1% to 2% is common. It doesn't sound like much. But take 2% out every year for 40 years (when you are likely to sell it to fund your retirement) means that the fee usually adds up to be more than 50% of your total gains. You took the risk with your money, and the people getting the fees get the profit for doing next to nothing. If instead you had a 0.2% yearly fee for 40 years, the fees are only about 7.5% of your total gains. Do you want to give up half of thousands/millions of dollars or 7.5%?
4) For that reason, many, many people recommend Vanguard. Low fees. Low fees aren't a guarantee that you will do well, but high fees are a guarantee that you will do poorly. Vanguard fees are about as low as you can get.
5) Also, consider mutual funds instead of individual stocks. Mutual funds let you own a bit of every company. That way if a company is an unexpected smash hit, making a killing, you own it. On the other hand, if a company goes bankrupt, you only own a tiny amount since your money is spread around everywhere, so one company going bad doesn't really affect you. It is the best of both worlds.
6) See what you qualify for that helps save taxes. Deferring tax, or avoiding tax altogether, makes investing easier (you can buy and sell when you want rather than worrying about tax consequences) and you can gain a lot more money without forking over the money to the IRS. That generally means:
6a) Do a company retirement plan just enough to get the free money from your employer.
6b) Next, invest in a Health Savings Account, if you qualify,
6c) Next invest in a Roth IRA (possibly a traditional IRA).
6d) Next finish out your employer plan, if possible.
6e) If any money is left, buy through a taxable account.