A .30-30 or .44mag lever-action rifle should do nicely. Based on your requirements (deer, multiple family members with variation in recoil sensitivity, support of "brushy" terrain, ease of adding a scope, low cost, ability to cover a SHTF situation in a pinch), a reliable lever-action rifle should cover the need fairly well.
Uncertain which calibers you have fired, previously. Particularly if recoil sensitivity is a consideration, I would suggest trying out a few first.
I'm partial to the .44mag caliber, myself. If 100 to 125 yds is your limit, I would think .44mag might be a serious option to consider, over .30-30. Something to think about, if recoil sensitivity is a concern.
A lever-action gives you the option of using the iron sights, mounting a scope in the standard position (with 3-4" eye relief), or mounting a scope or other optics in the "scout" position (forward of the "standard position, with ~8-9" eye relief). Some folks use a red dot sight. I've got a 2.5x fixed-power Leupold on one that provides a good field of view to support easy coverage of both shorter and longer distances. Great for shorter (< 125yd) "brush" situations.
In lever-action, I've basically got the same Marlin 1894 in .357mag, .44mag and (prevously) .30-30. The .30-30 was a carbine with 18.5" bbl, while the .357mag and .44mag are both 1894's in the "guide gun" (16" bbl) format. All of them are lightweight, well balanced, easy to maneuver in tight spaces. The 1894CP .357mag and the 1894P .44mag in particular feel wonderful in the hand.
If considering the .44mag, some folks have their lever-action rifles massaged by a gunsmith to accommodate the longer, heavier (> 300gr) bullets that handle busting through brush a bit better.
Nicely, the lever-action format supports a good range of caliber choices, as well. In basicallky the same rifle (ie, Marlin 1894 or 1895), you can find one in .357mag, .44mag, .45LC, .45-70, .308 Marlin. As you know, particularly in the common .30-30 caliber, you can find them for very little money. The .44magnums tend to be a bit more.
Have fun in your search!