I don't think we use Gillman's to create an enolate - we typically use Gillman's to add something in Michael's addition/1,4 addition/beta addition to carbonyls. It basically acts like a weaker nucleophile version of Grignards/organolithiums that preferentially attacks the beta carbon, assuming it's conjugated with the carbonyl.
NaOH is not that great for deprotonating alpha Hydrogens but we intentionally use this in things like "self" aldol condensations (aldols attacking the same aldol molecules) to deprotonate only a small portion of them and get them to react with the other aldols in solution. NaOH can also be used effectively to deprotonate molecules like malonic ester where the alpha Hydrogen is exceptionally acidic, e.g. here due to double resonance stabilization:
LDA is highly effective at deprotonating alpha-H's, so if you use it in a solution where you want aldol condensation among the same aldol molecule, LDA would end up making all of them enolates and it wouldn't work very well (there wouldn't be any non-enolate aldols left to act as electrophiles). But, we also use LDA effectively by separating steps: use LDA on the first reactant to create the enolates that you want, then in a second step add in the electrophile you want to get attacked. If you see LDA used you can probably count on an enolate being created.
Alkoxides (that match the leaving group) work well to deprotonate the alpha Hydrogens of esters because even if the alkoxide were to perform a nucleophilic acyl substitution, it would end up forming the original reactant anyway. You'll see this used in Claisen condensations.
Those are the only ones I can think of off the top of my head for deprotonating alpha H's. But I have to emphasize, a lot of figuring out what's going to happen will depend on the context of the reaction. The answer choices will (hopefully) make it clear that you have an alpha addition reaction vs a nucleophilic addition reaction. The DAT is multiple choice, so use that to your advantage - there have been plenty of times where I've instinctively looked for a substitution reaction only to see from the answers that it was an aldol condensation or something along those lines.
Also, some of these reactions can be acid catalyzed as well, albeit less effectively - so you may not even see base reagents being used.