The only tile improvements that cost money are roads and railroads. In general, you're better not building these at the start of a game, until you have at least 1 other city (and hopefully at least 2 workers).
Both take gold but can supply gold by trade routes (and railroads give a production bonus), and offer the obvious advantage of letting your army move though your land faster.
No other improvement costs money, and any tile, no matter if you are working it right away or not, can be improved for future use safely, without hurting your early economy, though it's obviously better if you are improving tiles that will make a difference right away.