thats the thing about shooting factory ammo...you either "settle" for how a particular load shoots...or you spend money on more different loads/brands etc and see/hope something shoots better...i shoot alot..and own a gun or 2...best thing i ever did was start loading my own...
i cant help much with scope in the lower range...im a Leupold guy myself...
but i'd say "on a budget" the BEST option would be to watch ebay and find a used vari-x II or VX-II...deals can be found...and a used one in the 3-9x40 will run 250 or less..typically 225 or less..i can almost always find a nice clean one for 225 or so...thats what i'd personally do...and if something is wrong or goes wrong, Leupold WILL make it right...cant say that about many other companies...
i learned a VERY hard lesson to learn about cheap scopes...long story short, i wounded and lost 2 deer and completely missed another all in the same season due to a junk scope...sure good scope can fail too...but, they are made much better, and are much clearer and brighter...
even my III series Leupold is noticably brighter than the II's...personally id buy a used II before a I or rifleman series....
1 good scope will last a VERY long time...and in the end will save headaches and frustration...and once you look through GOOD glass, its hard to go back...i wish both my VX IIs were IIIs after buying my first III...the IIs are great and more than good enough...but my III is just a bitttt brighter and clearer...which i didnt think was possible after using IIs for 10 years..but my new ones are all likely to be IIIs now..but, wont get rid of the IIs...great glass
but, i swallowed that season and learned a very tough lesson...and now wont skimp on glass...only gun that doesnt wear a Leupold is my 22lr and thats just because i dont use it a ton and havent gotten around to buying a good scope for it...and really, no recoil on a 22 so you can get away with a low end scope on them usually...