The cheapest way to have a flower garden is to grow the plants from seed. Some flowers are easier to grow from seed than others.
Flowers are classified as annuals perenials and bi-annuals. Annuals are usually the easiest to grow as they flower in the same year as you sow the seeds but they only last for one year then they die. However if you let them go to seed next year the seedlings will fill the area with flowers. Some flowers are good at setting seed in the garden. Others are best if you collect the seed heads and store the seeds n a cool dry place over the winter then sow the seeds in seed trays in the spring. You then transplant them when they are strong enough to survive in the garden and the weather is suitable.
Aqualiga is a good plant to try,as it seeds freely, cornflowers are easy to grow, love-in-a-mist and candytuft. If all else fails sunflowers in different varieties are the simplest of all.