Im moving to the states in 5 months but would like to start investing in US companies, namely through dividend reinvestment schemes. Are these limited to US citizens or can I start investing from before I move out there?
There are two kinds of dividend-reinvestment plans. The first is offered by the company you're buying. If you want to be enrolled in this plan, you need to buy stock in the company directly, and maintain multiple accounts (one for each company's stock). The details will vary from company to company, and can have some major downsides, especially when it comes to figuring out how to do the tax reporting. You'll need to find the prospectus and figure out whether you're eligible for the plan by yourself.
These plans are probably best for people whose main set of investments are managed by another party (e.g. a university pension plan) and who want to supplement this with some investment in just one or two companies that they know very well, because otherwise it's hard to get good amounts of diversification.
The second kind of plan is offered by your broker. Brokerages will charge you some money to trade stocks, but they are great because you can have one account with lots of stocks in one place. But unless your broker has a presence both in the US and the UK, you'll probably need to transfer your holdings to a new institution sooner or later. This usually involves a fee for the outgoing transfer (typically on the order of $50-$100). Additionally, the brokerage will liquidate any partial shares (theoretically these shares don't really exist individually; whole shares are held by the brokerage, and interest in those shares' value is assigned to people who hold partial shares). If you're enrolled in a dividend reinvestment plan, chances are you'll have some of these partial shares, and you won't gain or lose much by having it as 'stock' for a few months instead of 'cash'.
In the short term, I would recommend either storing your money in other instruments, or (if you think you can get much more than $50+ in earnings over the next several months - depends on how much you've got) buying individual stocks at a brokerage. When you move to the US and select a brokerage there, you can enroll in a dividend reinvestment plan offered by the broker and combine the cash you've earned from dividends with future investment cash.
There is no tax advantage to using a dividend reinvestment plan (and indeed, if it is in a taxable account, it may complicate cost-basis reporting in the future if you have to report a large number of small purchases).
This assumes you're interested in owning individual stocks. It is also possible to find yourself a stock ETF or mutual fund. Most mutual funds are pretty good about letting you reinvest your dividends. If you're interested in a diversified instrument where you can buy dividend-bearing US stocks, I'd recommend that you obtain an account at Vanguard (which is renowned for low expense ratios on its mutual funds) once you arrive in the US, and put money in a mutual fund such as the Vanguard Dividend Growth Fund or the Vanguard Dividend Appreciation Index Fund. (Naturally, you may also select other funds or fund providers based on what your research suggests meets your needs. Read the prospectus and understand the risks and potential returns.)
Of course, you should also consider whether a highly diversified investment strategy involving the whole US stock market (or even the world stock market), and not just US dividend-oriented companies, might be more suitable for your needs. Or a blended portfolio involving both stocks and bonds.
You can invest in the US as much as you want. Make sure to get an ITIN from the IRS and to fill the W8-BEN form for each company you're investing in (if directly) or broker (if investing through a broker), and you're good to go. When you become a US resident (for tax purposes, not immigration), make sure to replace the W8-BEN forms with W9's everywhere.