Okay Amy, from a woman's standpoint who doesn't understand the intricacies of this important task, I hired experts as it seems you will too. So, if you are trying to get a general idea of how it happens, I can tell you. We just had something similar done 3 weeks ago. But on a MUCH smaller scale, I might add. I had a load bearing wall between the kitchen and DR that we wanted to make more open. It supports at least half of our house. We went from a 36" open doorway to approx 80" open. The GC took measurements and found out the size of the header beam that the load required, structurally. When the time came, the carpenters opened up the walls and ceiling, moved the electrical out of the way and installed two temporary walls on each side of the existing ceiling/walls against the attic joists (we have a single story ranch so this might be different for you)Once everything was in place and the load could be essentially transferred to the temp suppports, they sawed thru the existing beams and installed the new longer heavier beam. I ended up with a new 12" deep header where I used to have two walls and an open doorway. It was either that or go into the attic and cut the joists to install a steel beam to carry the load if I wanted a flat ceiling. I opted for the less scary (to me) and more cost effective header :) Also, I googled 'removing a load bearing wall' and watched a few YouTube videos ahead of time so I could kind of understand the process. HTH!

If expenses are a concern, then avoid moving the sink from underneath it's present window. Put that money that you would have spent doing that into putting a beam to remove the load bearing wall. Just moving the sink down to the other windows only to put a range in front of where the sink is currently makes no sense spacially or economically. If the goal is to open the kitchen up to the other rooms with a minimal amount of expense, then you should consider leaving some of the wall intact to have a smaller beam. This would actually extend the wall, and force some different traffic patterns such as walking through the dining room to the kitchen from the garage, etc. What this would do though, is drastically reduce the cost of taking down that wall because all of the spans that have the be done from point to point here can be done with smaller dimensional lumber rather than any beams. Smaller and shallower headers mean more visual height, and they mean that a one or two man construction crew can handle the job rather than having to have 5-6 handle the logistics of doing a large beam. And, since the only plumbing addition is a prep sink and you're not moving the cleanup sink, there is savings there as well.

You have a beautiful home. Here are some Houzz pictures that might give you some thoughts for the trim work: [Traditional Living Room[(https://www.houzz.com/photos/traditional-living-room-ideas-phbr1-bp~t_718~s_2107) by Bonita Springs General Contractors Harwick Homes [Contemporary Kitchen[(https://www.houzz.com/photos/contemporary-kitchen-ideas-phbr1-bp~t_709~s_2103) by New York Interior Designers & Decorators Shane D. Inman [Traditional Living Room[(https://www.houzz.com/photos/traditional-living-room-ideas-phbr1-bp~t_718~s_2107) by Woodbridge Architects & Building Designers Huestis Tucker Architects, LLC [Traditional Living Room[(https://www.houzz.com/photos/traditional-living-room-ideas-phbr1-bp~t_718~s_2107) by East Anglia Architects & Building Designers Paul D'Amico - Period Design Do you plan to have some type of cabinetry or storage built in below the cutout, or will it be more like an interior window?

If you are looking at LVL beams, you should have a table similar to this one, which gives you the guidelines for height and width of beam required. https://www.weyerhaeuser.com/application/files/8514/9517/9127/1484260463_TB-551.pdf  Based on my reading of this table (maybe I'm not correct) you may need quite a bit taller or thicker beam for the span. You also need to determine how the load transfers to the floor underneath, and verify that it has sufficient strength. The original wall had multiple points in the floor evenly supporting this area, and now you will have a post that puts a much heavier direct load on a small area. You may need a basement support below, or thicker concrete under that post. Do your calculations and plan, and then hire a structural engineer to verify the calculations and sign off on the plan. This will reassure you, and keep the AJH happy. The reason I suggest getting the data together yourself first is that engineers don't all work on this type of homeowner construction job, and its better to simplify the question for them. If the engineer has to find the load tables for your specific brand of LVL beam, and do all the other data gathering himself/herself (find data on supports under the post, etc.), it will take that much longer. Bruce