We started feeding "solids" with home cooked and pureed veggies, bananas and other fruits, and yogurt, then moved on to include cheese and meats.
Our kids didn't have solids till around 6 months, and didn't eat much in the way of solids until closer to 8-9 months when they could self-feed.
Breast-fed babies don't need any supplemental foods until well past 6 months, our doctor recommended we start at that age with our first because she wasn't exclusively breast-fed (due to latch problems I never produced enough for her so we also fed her formula--and she wasn't much better latching onto a bottle than the breast so she moved up to a cup quite quickly).
Both of our kids really liked certain things (peas, melon and especially bananas--neither one like carrots as infants but both like them now). Both also really enjoyed chicken/turkey and meatloaf/hamburger patties as they got old enough to eat these meats.
We did occasionally feed rice, barley and oat cereals, but not on any kind of regular basis--mostly because infant cereal was expensive and our doctor (who was very progressive and was trained in New Zealand) didn't place emphasis on cereals.
I have never cooked liver because neither hubs nor I like it (it's actually genetic whether or not you like liver) and our kids didn't have eggs, fish/seafood, strawberries, peanuts/peanut butter or any other typically "allergenic" foods until well after 12 months of age. We introduced grains in the order that our doctor suggested: rice, barley, oats, wheat--and didn't start grains till 7 or 8 months.
I had to look all of this up in their baby books, because they are now aged 14 and 15 and all I could really say for sure from memory was that they liked peas, bananas and meat and didn't start on solids till after 6 months.
I would suggest that it is most important to ensure that your child is growing well, hitting benchmarks within the suggested timeline, and that you avoid potentially allergenic foods as you introduce new things to baby. If you are able to breast feed, baby won't need supplemental nutrition till well after 6 months of age, and then it was always suggested to me that one start with veggies so as to not introduce the "sweetness" of fruits before the more "savoury" tastes of veggies. General guidelines that served us well

neither of my kids has any allergies and neither is very picky about food (other than that the oldest doesn't like peas or for her food groups to "touch" on the plate and doesn't like sauces, and the youngest doesn't like cheese) and both are very open to world cuisines.