It will depends on what your preferences are, whether you're looking at a very mobile or semi-permanent set-up, and also whether you're after cheap and dirty or costlier but more reliable.
Instead of hurrying and just following what others say (everyone has their own opinion and preference), I suggest you take your time and slowly figure out what you really need, and how you would like to work. I'm assuming lots of studio sessions with your baby? Also assuming this is primarily for indoor use.
Starter lighting kits all in range from $1K+ to $3k (respectable, reliable brands)
Triggers - less than $100 to say $300+ (simple, reliable triggers and not the high end of very fancy ettl enabled stuff; often, special offers are packages with lighting kits)
From there, it's only a matter of getting a simple backdrop stand set, or wall or ceiling-mounted system and 1 or 2 backdrops. This should not cost you more than $250 and up depending on the brand, type and quality of the components you want.
Of course, these are very rough ballparks. A lot depends on whether you know what exactly you need and avoid unnecessary purchases, or whether you prefer to splurge of higher-end stuff.
There is always the option to buy 2nd hand. A lot of used home-studio equipment tend to be under-utilized and relatively well-taken care of.
Hope this helps some, and I'm sure other much more experienced members will be able to offer more details.