The idea of becoming a stock market millionaire need not be the stuff of fantasy. But if someone seriously wants to aim for a million, it helps if they have a plan.

A few factors are important – how much they can afford to invest, what their timeframe is and the shares they choose to buy.

The good news as I see it is that one can aim for a million even starting with nothing.

There’s no single right amount to invest

The more invested – all other things being equal – the sooner one can hope to aim for a million.

But there is not a one size fits all answer to the question of how much to invest. Each individual needs to make up their own mind about that, based on their own financial situation and priorities.

Indeed, one thing I like about shares is that, unlike some other investment classes, they can be bought with relatively modest sums.

One approach would be to set up a share-dealing account or Stocks and Shares ISA then drip-feed money into it on a regular basis.

Looking to the long term

How long it takes to get close to a million depends on the amount invested and the performance of the shares bought.

But what is clear is that this not some get-rich-quick scheme.

As a believer in long-term investing, my approach is to try and buy great companies at attractive prices and then hold them for years, or even decades.

A millionaire thanks to fewer than 10 shares

The importance of finding the right shares to buy cannot be overstated.

Say, for example, that an investor puts £800 a month into a portfolio that produces a compound annual growth rate (CAGR) of 5%. It will take 38 years to reach a £1m valuation.

That investor could aim for a million in just 23 years if they can achieve a 12% CAGR, although that is no easy task and investors could end up achieving a lot less..

To try and do that can involve doing less, not more.

Instead of buying dozens of shares that do quite well, just focusing on a smaller selection from the same group that do very well could boost the portfolio’s overall performance significantly.

Finding shares to buy

That sounds simple in theory. In practice though, does it require the benefit of hindsight?

Success leaves clues. Looking at past strong performers can give an indication of which shares could be attractive to consider now for potentially strong future performance.

For example, one share for investors to consider as they aim for a million is Alphabet (NASDAQ: GOOG, NASDAQ: GOOGL).

Its shares have stumbled lately due to tech valuation concerns and the risk of a monopoly investigation fining or even a break-up of the business.

When that happened to Microsoft many moons ago though, it ultimately came out stronger.

Alphabet is a money-making machine and I reckon that it could get even better over time, although regulatory challenges are a threat to profit margins. It has a large user base, unique service ecosystem and wide range of proprietary technology.

Even after recent falls, Alphabet is up 141% in five years. But long term, I still see it as a share to consider.