I want to get one lilac and I wasn't aware that there are different kinds. I live in New Jersey, the soil is clay and acidic. I want to place it in front of my house where it gets half day full on sun.
Also, my main concern is, I'm highly allergic to bee stings, so if it attracts bees I'll need alternative plants, one that smells nice but doesn't attract bees.
See attached pictures of the plants I'm interested in getting.
All the varieties of lilac you show in your photo are considered 'dwarf' forms, usually only making a height of 6 - 8 feet with a similar spread. Of the ones pictured, the ones I'd recommend are 'Palibin' and 'President Grevy' because in my experience, in sunny positions, they flower very well. Bear in mind they are only in flower for a short time - 2-4 weeks at most, and for the rest of the summer, you'll just be looking at fairly boring green foliage, and bare wood all winter. Mandevilla, as already said, is tender, but it's also a climber, and needs something to climb up.
In regard to bees, your safest bet is to only buy plants that have double flowers - these are usually sterile, and are therefore of no interest to pollinating insects like bees. An example would be Kerria japonica, which has single flowers, but the variety Kerria japonica pleniflora has double flowers, see here https://en.m.wikipedia.org/wiki/Kerria_japonica. The first is attractive to bees, the second is not.
If you want to ask what to plant in a specific area of your garden, information like whether its sunny or shady, dry soil or always damp soil, windy or sheltered, and so on is necessary.
Lilacs have been a traditional plant in rural gardens and at least in Germany where I live, probably every farmer‘s wife had some in a sunny spot. Syringa vulgaris is so robust, it can even be found naturalized at the place of former human settlements and according to Wikipedia
[...] it has been selected as the state flower of the state of New Hampshire, because it "is symbolic of that hardy character of the men and women of the Granite State".
My first mental image when thinking of lilac are huge bushes like this old group in my neighbors’ yard:
(For scale: note the greenhouse and the Piaggio Ape.)
But like with probably all “common” plants, breeders have busily developed hybrids in all sizes (some as little as five feet) and of course with blooms in all colors from white to dark purple, singles or with double flowers. So read the label or even better, talk to your local gardener.
For soil, lilac prefers nutrient-rich soil and is not exactly a fan of “wet feet”, on the other hand, a well-established plant will even cope with hot and dry summers without extra watering. And naturalized plants get no extra care whatsoever. Note that the “dwarf types” and some extra-fancy hybrids can be a bit pickier and may dislike acidic soil.
Unless you have your mind set on a specific breed (I wanted a Mme. Lemoine), many gardeners will be happy to share an offspring of theirs: Look for new shots somewhere in the root area of the parent plant. You can dig them up and take it to the new place. That way, you will know what to expect, both size-wise and for flowers. Lilac doesn’t mind pruning, so you can keep it in check to a degree. (Within reason, of course.)
And for your bee allergy:
Good news. While some books claim bees will visit lilac, many beekeepers report that their bees won’t visit it. This fits with my observation. So unless the bees have no alternative, you should be pretty safe. Note that during the bloom phase of lilac, other (preferred) flowers are typically in abundance.