$400 isn't going to get you much of a scope,especially if your wanting to really shoot/see targets at long range. Scopes in that price range are great for hunting scopes,but not very good for long range.Most lack having enough adjustment capability to shoot past 600 yards.
The cheapest priced scopes will be fixed magnification like the SWFA 10x42,and if you are only wanting to shoot targets,they work great for that. High magnification fixed power scopes usually won't work very well if you want to go hunting with them at shorter range,they have a small field of view compared with a variable powered scope that can be turned down in magnification.
Mil-dot or Modified Mil-dot reticles are what most long range shooters like,since they give you holdover marks on the reticle that help the shooter with ranging targets,and allowing for windage changes easily.But you also need to learn how to use these reticles,and the distances in mils or moa that they account for in that particular scope.
You will want to get a scope that has turrets that match the reticle. Either a Mil/Mil or MOA/MOA. I prefer using MOA/MOA,myself.
Most cheaper cost scopes that have a Mil-dot reticle have MOA turrets,and although they can be operated by the shooter,it takes more time to learn the math between the two measurements.
You also need to decide on which Focal plane you want to have the reticle in. First Focal plane scopes are easier to learn mil-dot style reticles with because the reticle size grows with the target image as the magnification goes up.
A Second Focal plane reticle scope,the reticle remains the same size,but the target image grows as the magnification goes up,and you have to know what the reticle (dots) measurements are at the magnification you have the scope turned to. Most are set up to be read at certain magnifications such as 12x,depending on the scope,but if you know/learn how to do the math,you can use the reticle at any power.
First focal plane scopes cost more than Second focal plane scopes.
The lower tier of decent long range scopes starts off around $750 for variable magnification scopes. The Weaver Tactical scope is a very good starter scope,and it even has a First Focal plane reticle.They come in a 3-15x50 or a 4-20x50 scope.They also have very good glass in them.
The Vortex Viper PST has a great following,and they can be had in First or Second focal plane.
I like the Sightron SIII scopes,they only come in Second focal plane,but they have amazing glass,track/repeat excellent,and for the price are hard to beat. I have 5 of them,and have never had an issue with any of them.
For a mount,I'd go with a good 1pc base-Weaver,EGW,Ken Farrell,etc.,and the only rings that I will use are Burris Signature Zee rings.
Savage 10FCP-308 & 110FLP-25/06 Ken Farrell base's,Burris Signature Zee rings,Sightron SIII LRMD 6-24x50 scopes-
Custom built Savage 10-6.5 Creedmoor Weaver base,Burris Signature Zee rings,Sightron SIII MOA-2 6-24x50-