What Tom says is true. For example session musicians are not free. For me I might use an online mastering service if I had heard a lot of their work. However remote recording using session musicians I would be very very unlikely to use. Interacting with the session musicians is key and that is far harder to do remotely, though not impossibly. I write and record my own music, so I can see the temptation for solo lyricists... but that is where there is a degree of miss-selling of online song services.
I would go with plan A. Work as locally as you can and get to know local studio owners, session musicians, other songwriters, producers and bands and work with them. not just amateurs either.
The first step is finding people, on or offline, to work with. Growing your contacts is the biggest single thing you can do.
By saying "demo" it makes me think this is to send to labels and publishing houses, as if it were for gigs you would have a band (or at least the whole line up you need to perform), and if that is the case an online recording service really doesn't make sense apart from mastering services.
If it is for labels / publishers etc these days they really expect songs submitted as production-ready. That being the case avoid online recording services like the plague (like a studio that takes either lyrics, or lyrics and melody, and records the song for you. Often writers aren't happy with the results. The results could be used to approach publishers but not labels... but the results are very unpredictable. Additionally they are less likely to be interested in the songs than say a band that writes and records their own songs (or a band that records your songs) because their interest is reducing workload, minmizing risk, and maximizing profit.
Add to that sending unsolicited demos is about as useful as digging a hole and throwing your hard earned money in.
Far better to find other writers to work with and then find a band to play the songs, or write the lyrics for a band that is good at writing music.
With a band online recording is really not a viable option. For me this is either recording for vanity reasons, or to record a high calibre of session musician that either they or you cannot travel and it really is the last chance to get them to record their part.
In terms of local studios, yes a song package is okay to a degree, but unless this is vanity recording don't go near them unless you have words, music, a good idea of the instrumentation and arrangement. At least you then clearly know what you want and can easily interact with the producer, engineer and session musicians.
If you have a band then record locally. A quick and dirty recording will be cheap but only much good for getting lower end gigs. Mid-range recording prices are likely to be not much better. Higher end you have to have the minset that you are creating a finished product where standards are high.
If you are a lyricist, find a music writer to work with to create finished songs.
Take finished songs to bands. Then record them (well the band does, and they pay for it too. If you need a demo to let bands hear you are as well making a simple home recording using vocals and one instrument to accompany the vocals.
Very rarely you will find a publishing house interested in a raw and rough demo. Usually they then get you to get it recorded properly before they invest. So you might as well focus on that before you start talking to them anyway.
Hopefully that helps. It's hard answering questions like this in a beneficial way. "How long is a piece of string" is pretty well impossible.
What is the purpose for the recording?
Can you create a complete song, words and music, or are you part of a songwriting team that can?
Do you have complete songs ready to record?
Do you work with a band that plans to do something with your songs?
What is your own level of music skills/knowledge?
What are your long term goals for your music?
Out of ten, how committed are you to do something with your songs?
With answers to those questions a better guess to cost could be made.
I regularly see writers, musicians and bands online that simply think high standards aren't needed, or they point each other to cheap services because they are cheap. That is simply lack of insight, laziness, and the delusion that labels, publishers, production houses and fans are happy to listen to poor quality music, and plenty of it. They don't.
Think about what you want and why you want it and then work towards making it happen. If you do you are far more likely to achieve your overall aims. That is unless you don't really care what happens. That being the case I would say save your money.