There are different bits of software available that mean that you can have all the information on your own pc.
Each of them have their pros and cons.
I don't think that there is one "best" piece of software. Different people prefer different things.
Here a couple of links providing reviews of the most common family tree software programs
https://www.whodoyouthinkyouaremagazine.com/feature/family-history-software
and
https://www.sog.org.uk/education/learning-hub/guides-tips/family-history-software/
There are three main, paid for, pieces of software (it's not a subscription though, just a one off payment to buy it outright)
Family Historian 7 (30 day free trial then £60 to buy)
https://www.family-historian.co.uk/
RootsMagic 10 (free "essentials" version or US$40 for the full version)
https://www.rootsmagic.com/rootsmagic/
Family Tree Maker 2019 (£80)
https://www.mackiev.com/ftm/
Or there is Legacy Family Tree 10 which is also free.
https://legacyfamilytree.com/
So what you would do is to download your tree from Ancestry as a GEDCOM file and then you can automatically import that into any software (or upload it to other sites like MyHeritage etc)
However, it's really important to remember that a GEDCOM files does not contain any of the sources that you have linked to each person.
So, all of the census records and christenings, marriages and burial records etc or any military records or workhouse records etc will not be included.
What you need to do before you end your Ancestry subscription is to also download all the records that you wish to keep. If you have a lot of census records, church christenings, marriage and burial records etc then you will need to individually download each of those.
If you have a large tree then that can take a very long time indeed. It all depends if you are interested in having copies of the original records or not.
"I rarely find anything new and interesting on Ancestry. Lots of very very distant relatives with Ancestry dna but that's about it."
What do you mean by new or interesting (serious question btw)? One aspect that I find intriguing is while I'm tracing dna relatives I come across people that have been involved with historical events.
For example, a number of my mum's older cousins were war brides. Just about every female member of my extended family that could grab herself a US soldier or airman in the 1940s and later the 1950s did just that and went off to the USA.
Then earlier in the 1900s I found someone who was forcibly emigrated from the UK at the age of 14 (he was in a workhouse) to go and work as an indentured servant on a farm in Canada. This happened to around 100,000 children from workhouses and orphanages in the UK.
Or if you have any male relatives born between about 1880 and 1900 then there is a reasonable probability that they served in World War One. This may not be so much of an interest but there is a great wealth of information available at The National Archives.
Or older relatives may have served in earlier wars such as the Boer War or the Crimean War.
Or going back earlier to the Mormons travelling to Utah. I found a few ancestors who followed the Mormon Trail to Utah in the 1850s and now I have dna relatives on both sides who live in Utah
Both my parents have also done their dna with Ancestry and this makes a big difference. Ancestry says that I have 16,400 matches. My mum has 20,200 matches and my dad has 18,800 matches.
So, just by going back one generation the number of matches I have has more than doubled from 16,400 for just me to 39,000 (20,200 + 18,800) for my parents combined.
"Lots of very very distant relatives with Ancestry dna but that's about it."
In contrast, it's finding the really distant relatives that keeps me interested.
To be fair, finding a second cousin once removed isn't so much of a big deal but tracing a 9th or 10th cousin based on dna was quite an interesting challenge.
If you enjoy solving puzzles, crosswords or sudoku etc, it's just another puzzle.
To be frank, the very distant relatives are not usually so interesting themselves, but the hunt for them and who I find along the way can be really interesting (this is how I found the examples above).
Most of my family have spent the last 400 years living within about a 30 mile radius of one city in the west of England. So it's interesting finding out about the ones who left. One example is two cousins who went over to America in the 1650s. They both ended up growing tobacco in Maryland.
Then, tracing their descendants you are suddenly hit with the reality of slavery.
For example, in the 1830 US Census, a branch of the family that had moved from Maryland to Georgia. They were a farming family aged 31 & 22 and had two young children. They also had two slaves; one was a boy aged between 10 and 23 and the other was a girl under the age of 10 (those were the age categories in the census).
So it seems that they maybe had a teenage boy slave to work on the farm and a young girl slave to help care for the children.
Then by the time of the 1840 census they had seven children and eight slaves. Two male slaves, presumably to work on the farm. There were also three adult female slaves and three girl slaves under the age of 10. I suppose they looked after the seven children of their owners.
When it came to 1850 the family now had eight children and 14 slaves. Although two of them had just been born. In the 1850 Census the sex and age of slaves were recorded, but not their names.
Just stop and think about that for a moment. Even in 1850 in certain states they are not even recording the names of slaves.
They had seven male slaves, aged 55, 30, 18, 16, 7, 9 months, 6 months.
They also had seven female slaves, aged 35, 30, 16, 11, 10, 10, 6
Then in 1860 they had 18 slaves, but still no names are recorded.
Nine male slaves aged 65, 40, 38, 25, 25, 23, 16, 12, 5
Nine female slaves aged 46, 38, 25, 20, 20, 3, 2, 10 months, 6 months
Slavery was finally abolished in the USA in 1864.
I found all this from just tracing a distant dna relative. The relative was entirely unexceptional (as I am if they tried to trace me) but the process of finding them and what I learnt on the way about how different branches of my family lived has been amazing.