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Everyone seems to want to spend your money with AF lenses and zooms that while fast aren't really that fast
Super Tak 50 f 1.4. fast cheap and excellent rendering. certainly fast enough to give you shots in iso 400 light. Babies don't really move all that fast so no reason you can't use MF lenses. If you decide you really like the focal length but just have to have AF down the road you can easily sell the tak for what you paid and put the funds towards a FA 50 f1.4 which is the modern equivalent
this was shot in a very dim lounge with minimal stage lights at f4 actually iso 400 (sorry no baby examples)
Cheaper still is the M 50 f1.7. this was iso 1250 outside on the dimly lit street at night f 1.7