Cauling is a step that is critical to the longevity and aesthetics of a good paint job. For the residential user there are commonly two types of caulk, both of them clean-up with water. There is the hand squeeze tube style and the caulk gun cartridge style. The cost of materials of a paint job is small compared to labor/time costs.
You will come out far ahead by using good quality materials that will perform and last much longer than their cheaper counterpart. Buy a good 45-60 year caulk that will not harden, crack or fall out after the first year.
You will want a ‘siliconized’ acrylic latex caulk, but never apply a ‘100% silicone’ caulk in a painting situation. Paint will not stick to silicone. We have used Kelly Moore’s squeeze tube caulk and caulk gun KM45 and KM1126 for years and had great success.