Under almost all circumstances, the only way to qualify for the Disney Dining Plan is to book a Disney resort package. Disney defines a package as a bundled purchase of room + tickets. The ticket purchase doesn’t have to match the length of resort stay; you can buy a package that includes only a 1-day ticket, if you want.
Buying an extra 1-day ticket is worthwhile when there is a promotion for the FREE Disney Dining Plan, but if you are to purchase the Disney Dining Plan, it would be financially unwise to have to spend $85 or so (for a 1-day ticket) just to qualify to pay for the Dining Plan, if you know what I mean.
If you aren’t an experienced Disney traveler, and therefore if you aren’t sure exactly what you’ll be doing in the future, my strong advice is DO NOT buy tickets a la carte. The small discount you might find (maybe $20 or $30 per person) could possibly be dwarfed by the savings you might find with a discounted package deal later on.