How much should I ask for/offer?

This is where you have to take a step back and assess your goals. You can hold out for the best financial terms possible, or you can reach an agreement sooner than later, but it's not usually possible to do both. 

In trying to reach a settlement, you're dealing with dividing the marital property and debts, deciding what if any alimony should be given, and if there are kids, determining a parenting schedule and a child support amount. In reality, these different goals are all interrelated in the final picture of what your post-divorce life will look like. But it's important to be able to separate these aspects of the settlement in establishing what's fair. 

In my place as an attorney, my default is to help you reach the most financially beneficial settlement agreement you can, and if an agreement can't be reached that matches or exceeds what I believe you could be awarded by the court, to prepare and take your case to trial. Many times, that's what's best for you and your family, and that's exactly what happens. Other times, the emotional benefits of avoiding court and resolving things quickly has enough value to the client that what you want - and what my job is - becomes doing the best we can, understanding the value and consequences of the agreement - and moving forward. This is a situation where it ultimately comes down to what you want, as you and your family will be the ones living with the outcome. 

That being said, with most marriages, the starting off point is half. We first determine what the assets of the marriage are (anything bought with money earned by either party during the marriage), placing value on them, and dividing them equally. Sometimes, there are good reasons to move away from a half-and-half split, but this is usually the starting off point for negotiations. The problems come up in agreeing on valuations of different assets, which party gets to keep certain assets that both (or neither) want - typically the house, which assets should or shouldn't be included for whatever reason, and things of that nature. Those are all valid considerations. But the key things you'll need to decide are how much do you need, how valuable is it to you to wrap things up quickly, and how important is it to keep things amicable. This is where an attorney can help as a counselor. Once you know what you want, an attorney can help you understand the pros and cons of the plan, and execute it in such a way as to eliminate unintended consequences.