The main problem with investing small sums is that trading fees can take up a larger percentage of the total. For example, if you invest $100 and are charged a flat $5 fee, you retain $95 in your investment. If you invested $5, you retain $0. (Fees can switch to a proportional basis for larger sums invested, but they are often a flat rate at the lower end.)
It only gets worse if you split a small sum among several stocks. $100 into 1 stock at a flat $5 per trade nets you $95 of stock, but the same $100 into 20 stocks nets you $0 of stock.
One strategy would be to pick any of your stocks to start with - but keep it to just one stock each time. You avoid the multiple-fee trap at the cost of diversification. The next round can be invested in a different single stock, and over time, you’d get the portfolio you aimed for.
Another approach is to find an index fund that sufficiently matches your ideal portfolio. Keep investing in that (one) index fund until you’ve built up enough equity to diversify manually, then sell the index fund and buy your individual stocks in the desired proportions. You get diversification at the expense of precision (and you might have to pay management fees, but some index funds can have low fees).
You can, of course, keep everything in cash until you’ve built up enough money to execute your strategy. This gets you diversity and precision at the cost of time in the market.
Disclaimer: the above is not to be construed as financial advice. Please seek appropriate professional advice before investing.