I would say your chances of a first job are slightly improved by going to CCAT. Most companies seem to prefer CCAT or OAT graduates even though all students end up with the same CAA approved qualifications - a load of old b**ls that shouldn't happen, but a fact.
There are companies that will recruit 200 - 250 hours people straight out of training schools. Mainly turboprop opertors like Flybe, BA Citiexpress, Eastern Airways, Scotair. And graduating out of CCAT with good passes will give you a slightly better chance than those using less well-known schools. With a disciplined military background you will be attractive to these employers compared with some "less mature" graduates.
I gave up a good career and took the plunge 5 years ago (also 29 yrs old then) and got a TP job with 230hrs having done a modular course. And the job market is better now than then, so there is hope despite what F-Nav says.