Personally, having been acquainted with Lincolnshire in the past, I would give it a miss. It has some very cheap housing and yes, it's countryside, but it's flat, bleak and depressing. Truly, it really is.
For about a month in the year it's sunny and quietly rural, for the rest of the time the flatness is awful. It's farming country but very arable, so yes, the fields are full of cabbages and potatoes, muddy for much of the year....not so many animals (eg. nothing like the lovely sheep filled hills of the Cotswolds).
Because the area is flat, the winds whip in and it can get very cold, even in the summer. Facilities are few and far between so the hospitals are poor, you have to drive for miles and miles for shops, for things for the children to do or just for the kids to see friends. Small children are bussed to school in the remotest parts from age 5 and so have very long days.
Boston itself is dreadful. It's run down and there is a lot of crime. The local people are very traditional and don't like change, there isn't a good population mix. However, there are overseas workers who come in for the farm work, and there have been clashes between them and the locals who don't like "foreigners". In addition, there is a high proportion of mental illness in the area. This is because Boston hospital is the only large facility for miles around so all the problem cases are sent there. They are then housed in the surrounding area to be near to the hospital and this causes an imbalance in the health of the local population.
Spalding isn't much better, it is another remote and bleak area situated in the middle of the "fens".
Lincoln itself is slightly better. The cathedral and original town buildings are picturesque and sit on the only high spot in the county. As one previous Bishop described the city : a nice cathedral sitting in 1000 square miles of bugger all !! Lincoln also has has a surprisingly high rate of drug usage, owing to it (and the county) being served by the A1as a drug trafficking corridor...rural 'county lines' drug problems are rife.
You will get cheap housing all over the East Midlands, Nottinghamshire is good (but watch out for some areas and there is crime and a high student population in the city itself) Leicestershire is utterly beautiful countryside although I would avoid Leicester itself and the A46 corridor.