I'd recommend Alex Plus acrylic latex caulk from DAP for most DIY projects. It's paintable, durable, non-hardening, has a long work time and is readily available.
For sinks, tubs, showers, etc, I use DAP Tub, Tile and Basin caulk. It's non-paintable, but has the other attrributes above.

randy's choices are close---I use GE kitchen/Bath caulk.

As important as the type of caulk is the prep for applying the caulk. Do a LOT of research on specific directions/recommendations for applying non paintable caulk---simply because if the surfaces are not absolutely pristine and clean, that type of caulk will not adhere. Very often, those surfaces need more prep than the simple 'clean and dry' mentioned on the label.

Scrubbing with alcohol/thinner/weak acid is necessary in some cases.

Thank you both.
I will do some more research on the prep portion of it.

I've also seen silicone & transparent caulk - when are those applicable to use?

Paint won't adhere to Silicone caulk. Silicone transparent is used when colored caulk isn't desired.

Got it now.
Thanks randy427.

Polyseamaeal, all the properties of the dap product, for a longer period of time, all paintable, excellent adhesion and tools with your dampened finger.

Silicone work best 20ft deep in a land-fill, unopened.

Silicone has poor adhesion to porous materials; it works best on clean non-porous surfaces like metals and tile. It also cannot withstand immersion in water for long. But it is very stretchy.

quote)Silicone work best 20ft deep in a land-fill, unopened.(quote)

As a painter, I can appreciate that remark!