Learn German: Der Plan ist zumindest besser als nichts. - The plan is at least better than nothing.

Zumindest and wenigstens can often be used interchangeably to mean "at least" in the sense of looking on the bright side or establishing a minimum acceptable condition, just like in this sentence. Mindestens, however, is strictly used for measurable quantities and numbers (for example, mindestens drei Tage for "at least three days"). Using mindestens here would sound wrong because "better than nothing" isn't a quantifiable number.

Could I say besser wie nichts in everyday spoken German?

You will sometimes hear native speakers use wie instead of als with comparatives in colloquial speech, but it is grammatically incorrect. Standard German requires als when there is a difference or inequality (like besser als, meaning "better than") and wie when things are equal (like so gut wie, meaning "as good as"). It is always safer for learners to stick to the correct besser als nichts.

Why is nichts written with a lowercase letter at the end? Can it ever be capitalized?

The word nichts (meaning "nothing") is an indefinite pronoun, not a noun, so it is written in lowercase. It only becomes a capitalized noun (das Nichts) when it refers to the philosophical concept of "the void" or "nothingness," usually preceded by an article or an adjective, such as in the phrase ein Sprung ins Nichts (a jump into nothingness).