When getting an umbrella stroller, pay a little more and get one that reclines. SO worth it. Even Lil will not sleep in a stroller that is up, but lay it down and she'll sleep anywhere. We have the Chicco Trevi and I LOOOOOVE it. It has a basket, a kid tray (a must have for us), it reclines fully, it has a huge sunshade, it folds up small (not as small as some umbrellas though), and it has a parent pouch and cupholder. Cons: It could fold up smaller, I would LOVE a removable seat liner and the parent cupholder falls off sometimes (not during use, during folding up and down).
Best big carseat ever....Graco Nautilus 3 in 1. It think it doesn't start until 22 pounds, but from then on, its the only carseat you'll ever need. Its one of the longest 5pt harness carseats and then goes to a high back booster, then you can take the back off for a regular booster. Watch for sales when she is getting close. go to www.babycheapskate.com and watch for deals. she posts deals on gear, toys, diapers, wipes, etc. Each week she will tell you where wipes and diapers and formula are cheapest and if its just a sale or if its a "stockuportunity"
Get a jumperoo or a walker. You don't need both. If you have mostly carpet, its pointless to get a walker.
We have a single Graco Quattro Tour stroller and a Graco infant seat. By far my favorite travel system, I had one for Lillian, sold it on craigslist, tried a Peg Perego, Chicco and some random one before going back to Graco Quattro Tour for Ellison. Best full size single stroler ever in my opinion.
We also have the Graco Quattro Tour double stroller. Now, I will be the first to say that unless you spend many hundreds of dollars on a double stroller (like a BOB), its going to be huge and bulky. That said, for the cheaper end of strollers, I love this one. I didn't want a side by side because we do lots of shopping and its hard enough to fit through aisles with a single wide. I like that the infant carseat can go in the front or the back (or both, if you have twins). I like that there are two cupholders for the adults and a pouch for stuff, as well as Graco's notorious large basket. There is also a snack tray and/or cupholder for both seats as well as a "treasure pouch". I don't like...that its heavy. Really heavy. But other than putting it into and getting it out of the van, I love it.