The 301 was designed in 1953 and released in 54 (Pre STEREO) this meant that Garrard had to play catch up with the new fangled 'illusion' of STEREO throughout it's production. Changes to the motor and spindle housing made some headway (The BBC changed their 301's to oil bearing for this reason). Garrard eventually brought out the 401 to meet with the requirements of STEREO (in culmination with the fact they had been flogging the same product for over a decade) Jump forwards in time and people began to realize that much of the 301's rough spots could be ironed out if the units were housed in the correct plinth. The sound of a well plinthed Garrard is engaging, energized and musical. I've heard lots of criticism but I've not heard the word dull or boring being directed their way. Rough & Ready might be one way to describe them. Very few people would venture to appoint the 301 as spectacular in detailed presentation. It is however possible to achieve some of this but it does come at a cost (detaching the motor from the chassis a la Bastin / RJC is a very good way to go) I can say with a decent Mono cartridge the sound of a 301 can be very nice indeed. However what you suggest as a goal is a good all rounder on a budget. Often you will see 301's paired with 12" arms and there is good reason for this the motor vibration is high and keeping the arm as far away as possible from this is logical and audible. A traditional pairing in terms of cartridges with the 301 is the Ortofon SPU. These cartridge are not neutral by any description I have heard or personally experienced. Coloured, warm, rosy, musical, tinted etc are often mooted as descriptors. Personally I think they have a nice flavor but perhaps not an every day flavor, rather like blue cheese - I love the stuff but I don't gnaw on it every day. The Low output MC Hana cartridge is a solid offering and good all rounder - Think cheddar. In terms of arms a second hand 12" Jelco may well suit, alternatively the Audio Creative Groovemaster MKII is an excellent, arm although potentially out of price range.
My apologies for the above cheese analogy, I am clearly peckish and acutely aware I have some crumpets and decent cheddar lurking in the kitchen.