Does your girl friend fish? That will impact your cost. You also have to consider travel cost and staying in a motel the day before departure from Anchorage to the lodge and then a motel on the return to Anchorage. With the girl friend along you may consider a few days in Anchorage and take in the sites.
If you can cast 40' and know how to mend your line you will catch fish. Some people go on trips that don't know a thing and still have a good time and catch some fish. The guides in Alaska are pretty much excellent and they will be a big help. Some lower cost trips put one guide with three people but most lodges have two people. It depends on if you are flying to a lodge and then use jet boats to get around. In this case there could be four fishermen to a single guide. If everybody in the boat is a beginner then that puts a load on the guide. That doesn't happen very often. Just make sure you know how to rig your setup and change flies. The guide will tell you were to fish as he knows where the fish hold in his water. He will also tell you what flies to use. Whoever you fish with will tell you what flies to bring. Most guides will have his killer fly and setup.
Considering your experience and budget I can recommend the Copper River Lodge. The fee for a week is $4300. I don't think they take non-fishing guest. They only take six fishermen per week and the river is fly fish only with catch and release for Trout. Late in the Season you can expect some big Rainbows. The river is easy to wade and that might be best for your girl friend. They do use jet boats for transportation with three fishers to the boat. This is one of Alaska pretties rivers. You can also arrange a one day fly out to the upper river to fish where there won't be other people fishing. This river has some dry fly fishing. This is a low pressure lodge with out the pressure you get on some fly out lodges that is always go, go, go due to weather problems.
You can check out the Copper River Lodge
here. If I ever go back to Alaska for another trip this is where I would go because of the easy wading, nice fish and limited fishers.
Another trip to consider is just a short fly out from Anchorage on the Talachulitna River. Beartracks Lodge
is located mid-river. While I don't know anything about the lodge I do know the Tal gets a lot of fish and has a resident population of Trout. Trout here will not run as large as you will find in the Copper. Their prices are very reasonable but they expect help from the guest with some of the chores around camp. Expect to clean your own fish. This would be more of a Salmon experience than Trout. The Tal gets runs of all the Salmon. I would choose later when the Silvers are running. You can stay as short as four days and you pay by the day so you can adjust the cost to fit your budget. They use jet boats to reach fishing spots.
A lot of Anchorage people float the Tal but the mid-river is the most productive. Years that have low water some of the floats start at mid-river instead of at the lake.
So there are two options just off the top of my head. Study the two sites and it will give you a feel of a full lodge and a kind of a do it yourself lodge. When you have a better feel of what you want to do we can consider may other options.