I would not write off the Dell Inspiron just yet... You may be able to order it online, but you will probably have to wait until Nov 27th when Best Buy updates their website to reflect the sale price.
The HP 350 G1 seems to be pretty good. If it is within your budget then go for it. It comes with Win 7 installed, but also has a license for Win 8.1; great if you do not like Win 8.1 for whatever reason. The Core i5-4210u can clock itself up to 2.7GHz when 1 core is used or 2.5GHz when both cores are used. That makes it potentially 600MHz to 800MHz faster than the Core i3-4030u which means it can last you longer before you feel that it is too slow and want to upgrade.
I do recommend that you install another stick of 4GB of RAM because it can help improve gaming performance by about 10%; but it depends on the game. That's because integrated graphics uses system RAM. When there is only one stick of RAM it operates at half speed which slows down the transfer of data a bit. Two sticks of RAM means the RAM will be operating at full speed to give around a 10% boost in performance; depending on the game.
Additionally, with only 4GB of RAM you may get warnings from Windows about low memory when playing game. For example, I play Star Trek Online with my 15.6" Dell Latitude 3540 which has 4GB and a dedicated Radeon HD 8850m with it's own 2GB of RAM. Even though the graphics chip is not using system RAM I sometimes get low memory warnings and a few time the laptop even freezes; not very often, but it has happened. Upgrading with another stick of 4GB of RAM solved that problem. However, Mass Effect 3 never gave me any low memory warnings.