I don't think you can compare football and baseball offers. There are 85 each 100% scholarships that go to each D1 football team as compared to 11.7 for baseball. In many cases, football players are making a choice between a 100% full ride here or a 100% full ride there. But, in baseball, full rides are rare...most position players get 25%-40% scholarships, pitchers get 40%-100%, and at least 8 players on the roster get nothing at all. As I said, 100% is EXTREMELY rare. I think football players know there is more money out there and do not worry about burning bridges. This has led to football players pitting one program against another and their verbal commitment means nothing. Even though that behavior has become acceptable or even expected by many in the football world, it doesn't make it right.
On the flip side, many baseball players, knowing that there is far less money to go around in baseball, find it hard to turn down money and accept the first offer given. Now, I agree with TPM, never accept an offer to save money, it may back fire if you are unhappy at that school. Just be open and honest with the coaches. Let them know where you are in the process, who is interested in you, who you are interested in, etc. Let them know if you need time to consider their offer and ask them how long you have to consider the offer. This is important because they have a signing priority. They may need an answer sooner than later. My son is a shortstop and the team he signed with wanted to fill that priority first. If you are honest with them they will be surprisingly honest with you about where they are in the process and how you fit in to their plans.
The scholarship, once signed is a commitment from the school. It doesn't guarantee you any playing time on the team but it is backed by the school even if the coach leaves before you arrive. Make sure you like the school first and foremost.
More specific to your question about visits, my son had 4 visits planned over a weeks time. We were planning to drive over 30 hours to visit all the schools who were seriously interested in him. We thought this would allow him to compare them to one another and make a decision while they were all fresh on his mind. He knew he would get offers at 2 of the schools once he stepped on campus due to the interest shown by those coaches. One of the schools, he did not expect an offer from (but loved the school when he visited for a camp), made an offer to him after taking us on a tour of the school and showing us the facilities. He said, "Dad, it just feels right". He wanted to accept the offer immediately, but I wanted him to have some time to think. He asked the coach to send the offer to him in an email so he would have something in writing. He told the coach that he was visiting some more schools and would finish his visits by weeks end. He asked the coach how long he had to consider the offer. To make a long story shorter, we did not finish our 30 hour drive. While driving he said, "Dad, if I really like the school (he liked it enough he had been considering walking on before getting the offer), and everything feels right, why visit the other schools?" I couldn't argue with him, especially since the school was 2 hours from home opposed to 6-11 hours from home like the other schools. We cut our trip short, drove home, and he called the coach and accepted the offer. He then called the other schools, and thanked the coaches for their time and interest in him, and told them he had accepted an offer and would not be visiting. All but one was complimentary of him and wished him luck in his freshmen year. One was mad at him for making a decision before visiting them. Once he accepted the offer, his response to future phone calls by coaches was, "I appreciate your interest, but I have accepted an offer already".
In the end, he was the one who made the decision. I believe he made the right one, and most importantly, went about it the right way. Confirmation: He started 50 games at shortstop his freshmen year, his team made it to the conference championship, and he loves his coach and teammates.
Here are some of the things my son considered (in addition to scholarship money) before accepting his offer: 1. Do I like the school? Would I like to attend this school even if I was not playing baseball? 2. Does it supply my educational needs? 3. Do I like the coach? What is the coaches philosophy, temperament, style? 4. What are my chances of playing immediately? Do they routinely red shirt freshmen or do they give them a chance to earn a spot? 5. What is the atmosphere/camaraderie like on the team? Do the players look like they are happy, like each other, buy into the program?
My advice, if these questions are answered in the positive, and you then choose to accept an offer to that school, then stay true to your commitment and your word.