One question with many answers. Here is my outlook.
Starting with bolt action rifles:
In the budget line you have a few nice contenders. Marlin just updated their bolt action line to the new XT line. Looks about the same and I would expect similar performance. Shoot well, compact, and handy rifles. Magazines feel cheap and hopefully the trigger is better than the old T900 trigger (which was horrible). It competes price wise with the base model Savage Mk II. This is another accurate, light, handy rifle for very little money. I believe Mossberg makes a budget bolt rifle too, but I haven't heard much about it and with the others in the class doing so well it's hard to take the chance.
If you step up in price point, to say the $200-$400 range you get yourself into some quite nice bolt rifles. The go to choice for many is the CZ line. They are one of my favorite for the price. I've owned 5 different CZ firearms from rimfire rifles to centerfire rifles to centerfire pistols, all being firearms I've enjoyed. You also get into some of the fancier optioned Savage models. I'm not sure on average if CZ out shoots Savage or not, but having both I enjoy the CZ's a little more when using them. I'm perfectly happy shooting the Savage and have no desire to sell it either. At this price range you also add in Ruger and their 77/22. This is a fine rifle with a beefy action. Older models weren't known to always be the most accurate rifle out of the box but they seem to shoot pretty well today and respond well to aftermarket work.
The used market is loaded with $400 rifles. You can occasionally find a used Anschutz 64 action at $400 which would be a fantastic rifle. You can find many Remington models in that price range. The 504 was a quality rifle with a few bad barrels that ruined the name. Some have been rebarreled and some decent from the factory. They would be a setup I'd take a gamble on. Then there are the older 513, 540, 541, etc lines that all shot darn good and were crafted very well. Some of the old Savage models were built well too. You can find old BRNO rifles in this price range which are similar to the CZ line. Great values. Some of the older Mossberg rifles were very well built as well. Winchester made many high quality rimfires as well. The used market may hold the best deals going to be honest. Many of those older rifles shot great and were built with a level of craftsmanship that can't be found on most of today's market, especially at $400.
The semi-auto market is flush full of good options too. The two big names are the 10-22 and the Marlin Model 60. Both are tried and true and have stood the test of time. The 10-22 can be more easily upgraded by the home user and the Model 60 is a rifle that asks for no upgrades. Remington has the 597 line in which most users seem to really enjoy them also. While the box mag of the Ruger is a very good system I feel it makes the rifle too wide. I like the slimmer lines of some of the other systems. Marlin makes a mag fed version of the Model 60 called the 795 which also has a good following, especially among those that attend Appleseed shoots. CZ has brought back and "updated" version of their semi-auto, now labeled a model 512. The old model 511 is my most desired auto-loader though the new 512 does not do quite as much for me. Thompson Center has discontinued their semi-auto rimfire line though they were known to shoot very well and be reliable. If one came by at a decent price I'd have it in my collection.
Then there are the lever action rifles. The 39A is the gold standard in this segment. You will be pushing the upper range of your price limit but they are well worth the cost. The Browning BL-22 is another quality lever gun. Henry makes a nice shooter. Not as well built or with the quality materials of the Browning or Marlin, but quite a bit less cost as well. I do believe Mossberg is making a rimfire lever rifle too but I have not experience with them.
There is also two classes of trainer rifles, one being the more recent semi-auto battle rifle clones and the other being the old Russian military trainer bolt rifles. The Russian imports are typically well built with a few quirks here and there. Great rifles to learn and build shooting skills with but not the most compatible with many non-Russian current production parts (sights, mounts, etc). There are semi-auto AR, AK, MP5, Sig 552, SCAR, and eventually STG-44 clones out there (may be forgetting some like MAC 11 and some others too). These typically have similar control layout and are a ton of fun. Most aren't overly accurate and are more about fast shooting plinking or up close speed drills than trying to shoot bug holes at 50 yards. I have a couple of S&W M&P 15's and they are a blast. If I had to pick the most fun rifles to shoot they are at the top.
In the end, most of today's current production firearms are decent to great. A very few are bad all around but the big names are all in tough competition and are putting out quality firearms. More money spent often buys more features and a slight increase in accuracy. The budget models should end up being good shooters and would be all that was needed to learn the fundamentals and beyond. The more expensive models add bells and whistles that makes use and ownership more enjoyable. The use market, especially from the 50's and 60's is full of well built, good shooting rifles at a bargain price. If you find an interest in any specific category you can narrow your search down. I'd head to the nearest large gun shop with a variety of new and used rifles, shoulder a few, and see what calls to you. That is probably going to be a bigger difference than anything else.