The Access is probably a decent frame. But I can tell you that a frame build will cost you so much by the time your done it will leave you scratching your head. I've done 3 of these a few years ago. Even the cheapest suspension fork will cost around $75. I guess you already have a headset, a set of decent 26" wheels, linear brakes, tires, seatpost, etc., etc. if you have never built up a bike, you have no clue the things that pop up. If you don't have a parts bin, it will cost you more than buying a good older $300 bike.
As for the Mongoose. Have no clue what year it is. If it is an older one it might be worth it. If it is a cheap Walmart bike, have fun.If, and it may be a big if, you can find an early 2000's Trek or Specialized with little use, (not abused) you will be much further ahead. 9 speed drivetrain, most forks were an improvement of those from the 90's, and cheap.If you need to keep the cost down due to financial reasons, I can appreciate your situation. If it is just to be cheap, but you can afford better, you are probably a bit too foolish for someone who had spent 60 years on this planet.John