The topic of what formula to use when breast milk is not an option generates a lot of smoke and heat, and is one of our more frequently-asked-questions ... so here it comes, folks, 2 level scoops of science mixed with 4 ounces of opinion.
I usually recommend a cow-milk-based formula at first. "But aren't all (insert-ethnicity-here) children lactose intolerant?" Actually, inborn lactose intolerance is extremely rare. Since lactose is the main sugar in breast milk, infants are born with the enzymes to digest it. While lactose intolerance may show up earlier in non-Caucasian children, you probably have at least 1-2 years of good ability to digest lactose. Also, an internationally adopted child has most likely already been receiving a cow-milk-based product, quite possibly sweeter, more dilute, and less nutritious than Western formulas. If you really really want to avoid lactose, and stay with a cow milk formula, there are lactose-free formulas, but they swap in corn syrup for the lactose.
Soy formulas are also an option, but in my mind you should have a compelling reason to switch. The long-term effects of a mostly soy-formula diet are not well-described; in the decades they've been in use, we've not seen obvious hormonal impacts from soy's phytoestrogens, and one retrospective study seemed reassuring, but we can't know that there aren't subtle effects. Also, certain minerals may not be as well absorbed from soy products, and children can get constipated on soy formula, neither of which is what you want in the first few weeks. I'm not that anti-soy, and do feel that cow milk itself is a bit overrated as a nutritional source ... but for infants I need a good reason to go with soy. For toddlers, where the soy is just part of a healthy diet, and lactose intolerance is a more real possibility, a soy formula could be fine if they don't tolerate dairy.
You won't see goat milk on my list of recommended formulas. Goat milk is well and good as a substitute for cow milk, but I've just seen a few too many infants starving on goat milk formulas. Perhaps it's that "make-your-own-formula" isn't the safest way to go, perhaps it's that people don't realize that truly cow-milk-allergic infants are also likely to be allergic to goat milk (and soy) ...
I also never recommend a low-iron formula, but luckily they're hard to find. Adequate iron is essential for cognitive development, and international adoptees are frequently iron-deficient.
As for DHA/ARA, which are omega fatty acids present at varying levels in breast milk that are felt to help brain and eye development, I will say that they make good theoretical sense, but the research outcomes have been more mixed than the advertising would have you believe. For international adoptees, there is no research on this topic, but it would make sense that they'd be deficient in essential fatty acids, so I do have a preference for formulas with DHA/ARA.
You'll be seeing more about probiotic formulas, now that Nestle has introduced an infant formula with probiotic cultures to the US market. I can't say that the verdict is in on probiotics and infants, particularly when it comes to which strains and doses to use, but there is mounting preliminary evidence that this may be a good thing. I don't think everyone should jump on this bandwagon just yet, but something to think about for adventurous early-adopter "natural" medicine type folk. Our article on probiotics has more, including some brands to consider, if you'd like to add your own.
I do recommend that newly adopted infants and young toddlers stay with formula as their drink of choice for about 2-3 months post adoption, and certainly to at least 1 year of age. It's just much more nutritionally dense than milk, juice, etc. Since many adoptees have micronutrient deficiencies (vitamins, mineral, iron), the formula can help. As for "toddler formulas", it's a trade-off: on the good side, they've got more calcium and phosphorus, on the bad side, the sugars are typically from corn syrup (unless you're convinced your child is lactose intolerant, then it's good). Confused yet?
Many parents choose to continue using the familiar local formula when travelling, which makes sense in terms of minimizing transitions. You can gradually switch to a US formula when you get home. However, I do think it's a good idea to bring some US formula too, in case you run out, or for children who don't seem too picky about such things. And for those adopting from China, I would switch promptly to US formula, even though it's likely that melamine is no longer in Chinese formula as of 8/08. For children getting rice cereal in their bottle, I would wean that too when you get home. Rice cereal is for eating, not drinking, and it won't "fill them up for sleep" (sadly).
If you child is refusing formula during your travels, please see our topic on Transitional Feeding Difficulties for some ideas. We also have an article on Nutritional Supplements in Adoption with more advice on vitamins, minerals, and essential fatty acids.
When it comes to specific brands, it's more about your philosophy and pocketbook, and your child's digestion, and less about science.
One last thing: use bottled water to reconstitute formula in developing countries, and consider doing the same in the US, at least for infants. It doesn't need to be designer water from artesian alpine watersheds, those cheaper jugs will do. Not that our water supply isn't the envy of many countries ... it's just that now the ADA has stated that using fluoridated water for infant formulas may overdo the fluoride. For toddlers, for whom formula is not the mainstay of their diet, I'm not as fussed about the fluoride issue, so filtered or tap water is probably fine. Brita and Pur-type filters remove a bit of the fluoride, but do leave enough for the water to be considered fluoridated.