What significator would you give to shops or stores in horary?
How about shopping?
Just a general question.

In terms of house I'd say 4th for the location itself, 5th for shopping if done for fun and not as a necessity, and maybe other houses related to what store is it? (say a clothes shop would probably be 2nd house).

In terms of planets, maybe Mercury, and again depending on what the store is about (say clothes shop, probably Venus).

I normally give necessities like food to the 6th house. Shopping is a chore like folding laundry so it seems very 6th to me but it would depend. If it is something for pleasure the 5th would likely work and Deb assigns food as 5th although in practice I usually see it as 6th in event charts so horary probably isn't different. It would depend on the context of the question. For example, if someone wanted to start a business that was a shop then I wouldn't use either of those houses.

You are right that planets would vary based on content. Mars would lord things like ironwork for example. I would probably give Saturn to home improvement because it lords home materials.

What significator would you give to shops or stores in horary?

It depends on the type of shop or store you have. Any planet can signify the type of business you are running. Or the type of stores you are looking for if you are a buyer.
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How about shopping?
Just a general question.

Shopping is generally a Moon activity. It stems from our mental activity and desires (Mercury and the Moon).
It is almost a daily activity whether you go to the grocery store or the coffee shop.
And the Moon has its Joy in the 3rd House of tradings and exchanges.
The 2nd House if you want to buy something
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Epicurus, a greek philosopher, distinguishes between three types of desires: natural and necessary desires, natural but non-necessary desires, and unnatural and non-necessary desires.
1) Natural and necessary are those that look to happiness, physical well-being, or life itself like food, clothings and a home. Love.
2) Natural and non-necessary desires are for pleasant things like sweet odors and good-tasting food and drink, concerts, sports etc.
3) Unnatural and non-necessary desires for great wealth or for marks of fame. These empty beliefs are the main source of perturbation and pain in civilized life.

If we think about his approach, you can buy a pair of shoes at all 3 levels
1) for walking (comfortable, resistant, practical)
2) for the color and the look of the shoes
3) You already have 5 pair of shoes but you want the Nike brand to impress your friends at school.

In terms of Houses, the 5th for shopping if done for fun and not as a necessity, 6th if for clothings and practical objects (tools and cooking ustensils). But any house can be involved as you may be shopping for a consultant 7th House (lawyer, beautician or training coach)

Tanit:
I would probably assign food (groceries and such) to the 2nd, as it is one of the things which sustain the body or the individual (just like money in a way).
The 6th seems to be too much of a problematic house for such a signification.
Although as a chore you might have a point there.
Those houses are connected by trine, after all.

Ouranos: Moon and the 3d house do seem to be quite important in those matters.

I consider it an entity I do business with. So perhaps the 7th?
I agree with what is said. The moon's next aspect could be so very important - much more important than rulership. I've done a few shopping-related charts and every time the moon was spot on.