We advise to start not with big names and costly works, but to follow some contemporary artists, see how they develop. There is a possibility that the artists will grow in value. Also one can start collecting works on paper and prints (multiple editions).
Follow the market development, but choose primarily what you love. Train your eye, pay a regular visits to galleries in your home city and while travelling. Follow up with the art fairs.
Choose quality over quantity. Certain circulation in the collection is possible, with the time a collector realises the corn of his or her collection, and can sell the unsuitable works.
If you've started to collect a contemporary artist, acquire the works in the galleries or on the open bidding platforms. Your support of the artist will encourage the price growth.