Hi, thanks for sharing such a thoughtful post. It sounds like you've thought this through carefully and your setup, with one of you part time and available during school hours, is actually one of the more workable arrangements we see.
On long term versus short term: your instinct makes sense. Long term fostering does tend to create more stability for everyone in the household, including your own children, because the routines become predictable and the foster child becomes genuinely embedded in family life. Short term or emergency placements can be rewarding but the uncertainty, and the goodbyes, can be harder on birth children than people expect. That said, some families with children your kids' ages do both successfully.
On age preferences, yes you can express a preference and it will be taken seriously in matching. School age children are among the most commonly placed. Wanting to place a child in a school your children already attend is a practical idea and worth raising early in assessment, though how workable it is depends on local school capacity and the child's specific needs.
Your husband's occasional travel is worth being open about in assessment. It doesn't automatically rule anything out, but it will be a conversation, particularly around what cover looks like when he is away.
The replies above raise fair points but plenty of foster carers in similar circumstances make it work. The honest answer is that it depends enormously on the individual child's needs and your own resilience as a family.
I work for Capstone Foster Care, an independent fostering agency. My response is only applicable to fostering with Capstone.