There's been some great discussion on mumsnet on this, as well as pps.
I'd say start with an open attitude but very low expectations... I hope you strike gold straight away, but many people are very busy/don't have time or energy to invest in a new 1-1 friendship. The people who are too available may be odd or difficult or needy. It really isn't you.
Like pps say, finding groups you enjoy can meet social needs.
Again, it may be hard to meet people for 1-1 but if the group is friendly and civil the low level contact may be enough.
Prepare for quite a lot of sifting and screening (some weirdos).
It's quite common for some groups to be a bit odd, or clichey, or your face clearly doesn't fit.
If a group is OK but not amazing and you enjoy the activity it may be worth sticking around. Often it takes a few months for people to adjust to you, or you to feel comfortable. Ideally you want something you can show up to regularly.
Agree to take a multi-pronged approach, have a few different things on the go for a few months .
Meetup? Lots on offer, although not all is good.
Co-working spaces are really taking off if you can work from a hot desk.
Spiritual? A lot of meditation centres, quakers offer a sense of community without getting religion involved or needing you to commit or practice!
Location can really make a difference, you may want to consider trying events or activities in the nearest city centre.
Stay in touch with your own feelings and emotions and don't have too set an idea about how things should look...
I guess the friendship "ideal" may be a woman or an all female group close to your age and similar to you. And you know all about each other and commit to meeting every weekend.
However, it may be a bit more patchwork/random than that as everyone is busy...Just go with the flow, and enjoy things on an ad hoc basis. Backed up with self care and some Internet chat it may be enough.
I also don't think you can have anyone but yourself to 100% rely on in times of crisis.
Even people with huge social groups say how it's often only parents/close family who REALLY are there for them in big events. You don't know who is going to be genuinely supportive or not, even if they profess to be your bestie!
But having some supportive networks of ok people and allies is definitely a realistic goal.