Although I own a tackle shop in a bag (my wife says I have at least 1 of everything that Bass Pro Shops has in the store), when it comes down to it I probably don't need most of it (OMG, did I just say that!).
So, if I was in your position with two small kids to entertain, this is what I would pick up (keep in mind, I mostly fish inland lakes for bass, pike, walleye, muskie, crappie, perch):
Terminal tackle - pre-tied aberdeen hooks, bell weights (1/4 to 1oz), swivels, split shot weights, bobbers, nail clippers, pliers to remove hooks, small first aid kit, screw driver, scissors, jig head poker thing (to remove the paint and open up the holes), stringer to hold the fish you catch!!
I'd also just stick to monofilament line for now, probably 6lb test Trilene XT. It works and has worked fine for a long time.
1) Jig heads - round head of various sizes - 1/32, 1/8, 1/4 and maybe 1/2 - depends where exactly you fish (depth, current). As for brand, well just get what's on sale IMO. The Bass Pro brand are good but not necessarily inexpensive, they have both an expensive and cheaper series. I prefer Owner, but they are one of the most expensive. Northland might be a good choice for a value brand. Matzuo aren't too bad if you can find them on sale. If you are near an independent tackle shop you might be able to pick up some locally made ones with decent hooks (Owner, Gamakatsu or Mustad hooks). I use unpainted and painted. I have yet to decide if it matters, many say yes - so, if you think it does go for white, yellow/chartreuse, pink IMO.
You can catch anything at any time of the year on Jig heads with live bait (worms or minnows) or...
2) Plastic Grubs - single tail. You will find an enormous range of brands and colors. Start with the basic colors, white (most definitely), black and yellow. A natural brown (pumpkin) or green (watermelon, green pumpkin) would be a good choice too. That being said, PINK is my favorite! Mister Twister is the most known brand (I believe they invented it?? I don't know). However, I prefer Yamamoto, but they are also the most expensive. I also really like Yum brand baits. They are inexpensive and I have had a lot of success with them. I own a ton of these things of various colors and sizes and textures. Most are Yamamoto and Yum, but I also have Kalins, Zoom, Lindy Joe, Mister Twister. I use the 3" and 4" most of the time, but have 5" for certain times and smaller 1"-2" for panfishing.
3) Pre-tied Aberdeen hooks - great to just toss onto a line with a lead weight and live bait or use a split-shot weight with a bobber. I do this for my daughter. There is a handy little plastic device that connects the hook and main line without tying too. I love them. Makes setting up and shutting down a breeze. I forget what they are called though, sorry. I bought them at Le Baron but I used them as a kid fishing Detroit River a lot. However, you can probably just get away with jig heads.
4) Live bait harness - this is basically a hook(s) attached to a spinner blade in line. Great for drift fishing with live bait for walleye. An Erie Dearie is similar and also good for the same purpose.
Now, for Dad when he wants to cast and retrieve - you can start with 1 or 2 lures from [all or some of] the following categories:
1) Shallow crankbait (<4 feet) - Can't go wrong with an original floating Rapala. The Rapala dives to series are nice and the shallow shad raps are also. Good for anything. I use these crankbaits on top of weedbeds in 8-10' of water.
2) Medium diving crankbait (8-10 feet) - There are a ton of them. Pick one or two you like from companies like Storm (I like Hot'N'Tots), Rapala (Shad Rap), Cotton Cordell, Rebel, Bomber, Bagley's, Manns, Smithwick, etc. Perhaps one chubby fat one and one slender one. Good for anything. Note: you can also add some split shots to your line and use the floating Rapala too! Sizes 3" for the chubby shad types, and 4"-6" for the slender ones.
3) Lipless Crank - Can't beat the original Rat'L'Trap. The new ones from Rapala (forget the name) look nice but haven't used them yet. Good for anything.
4) Slash bait/Jerk bait - Rapala also makes a nice slash baits, the X-Rap and the Husky Jerk. Storm, Smithwick and Bomber have some nice ones too. Good for pike and shoreline fishing for anything.
5) Topwater - There are a lot of great frog baits, both soft plastic and hard. Abrogast Jitterbugs and Hula Poppers are old school favorites. I like the soft plastic frogs a lot - some are basically crank baits but companies like Yum, Zoom make poured plastic frogs that you put on your own hook. You can't forget the Heddon Zara Spook for "walk the dog" presentations. Other topwater plug-type baits are great too. Storm, Smithwick, Rebel and Rapala make some nice ones. I use this mostly for bass fishing, but you can do this for many types of fish.
6) Spinnerbait - Great all around lure. Often used for bass fishing but will catch everything. White is a good choice. You can also buy plastic "chunks" that you can hook on to add bulk to the bait.
7) Plastic Cigar Worms - Great if you want to fish the weeds for bass. You will need some extra-wide gap hooks too (again, I like Owner, Gamakatsu in size 1/0 to 3/0). Yamamoto Senko are great, but expensive. I also really like Yum Dingers, which are much cheaper. I like White, Pink or Bubblegum swirl. A natural color like watermelon or pumpkin is very popular too. Plastic trick worms (long and slender as oppose to thick and fat) are good too, but are rigged differently. Although not a worm, tube jigs (Gitzits) are another option. Again, you need specific hooks (I use 5/0) or tube jig heads to use them. Good for all fish, but I use them for pike, smallmouth.
8) Spoons - I don't use spoons that often except when I go Pike fishing, but it works for all lake fish. I like Len Thompson, Daredevle, Little Cleo, Williams. Very popular for salmon fishing.
9) In-line Spinners - I also don't use in-line spinners that often. I do own a lot though (lol). Can't go wrong with any of them. Mepps, Rooster Tail, Panther Martin, Blue Fox come in various sizes depending on what you are doing - 3 is a good size all around. For trout, whitefish I believe you would use a 0 or 1.
In most cases, for crankbait/spinner color you can pretty much stick with white, silver and/or gold. However, I often pick up firetiger or perch pattern for cranks.
Of course, there are a lot of other options that really depend on what you are targeting, type of fishing you like to do, where you are fishing and in what season.
I probably just confused things more than anything, so from this list I think my shopping list would be: terminal tackle listed, 1/16, 1/8 and 1/4oz jig heads with plastic grubs (3 packs of 3" Yum in pink/white, white, black), 1 3/8oz white Strike King spinnerbait, 1 lipless crankbait (Rat'L'Trap silver, firetiger, perch or crawfish), 1 6" (F11) silver floating Rapala, 2 medium crankbaits (probably Hot'n'tot and/or Shadrap and/or a Bomber long A or Smithwick Rattlin' Rogue), 1 silver slash/jerk bait (Rapala X-Rap or Husky Jerk), 1 frog pattern topwater (probably a jitterbug - I love the sound they make), 1 Red/White Daredevle, 1 Mepps Aglia#3 Silver, 1 package of 5" Yum Dingers in bubblegum swirl and some 3/0 EWG hooks.
This article might help ya out too (a lot of the lures I mentioned are actually in this list): http://www.fieldandstream.com/photos/galle...-lures-all-time